[{"article_number":"2109.10203","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2109.10203"]},"author":[{"first_name":"Martin","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin","orcid":"0000-0001-5293-214X","last_name":"Dvorak"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"}],"title":"Generalized minimum 0-extension problem and discrete convexity","citation":{"ieee":"M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and discrete convexity,” Mathematical Programming. Springer Nature, 2024.","short":"M. Dvorak, V. Kolmogorov, Mathematical Programming (2024).","apa":"Dvorak, M., & Kolmogorov, V. (2024). Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. Springer Nature. https://doi.org/10.1007/s10107-024-02064-5","ama":"Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 2024. doi:10.1007/s10107-024-02064-5","mla":"Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” Mathematical Programming, 2109.10203, Springer Nature, 2024, doi:10.1007/s10107-024-02064-5.","ista":"Dvorak M, Kolmogorov V. 2024. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming., 2109.10203.","chicago":"Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” Mathematical Programming. Springer Nature, 2024. https://doi.org/10.1007/s10107-024-02064-5."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Open access funding provided by Institute of Science and Technology (IST Austria).","date_created":"2021-09-27T10:48:23Z","doi":"10.1007/s10107-024-02064-5","date_published":"2024-03-07T00:00:00Z","year":"2024","has_accepted_license":"1","publication":"Mathematical Programming","day":"07","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","keyword":["minimum 0-extension problem","metric labeling problem","discrete metric spaces","metric extensions","computational complexity","valued constraint satisfaction problems","discrete convex analysis","L-convex functions"],"status":"public","_id":"10045","file_date_updated":"2021-09-27T10:54:51Z","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"date_updated":"2024-03-19T08:20:31Z","ddc":["004"],"scopus_import":"1","month":"03","abstract":[{"lang":"eng","text":"Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n"}],"oa_version":"Preprint","publication_status":"epub_ahead","publication_identifier":{"issn":["0025-5610"],"eissn":["1436-4646"]},"language":[{"iso":"eng"}],"file":[{"file_size":603672,"date_updated":"2021-09-27T10:54:51Z","creator":"mdvorak","file_name":"Generalized-0-Ext.pdf","date_created":"2021-09-27T10:54:51Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"e7e83065f7bc18b9c188bf93b5ca5db6","file_id":"10046"}]},{"date_updated":"2023-08-21T06:49:11Z","ddc":["000","510"],"file_date_updated":"2023-08-21T06:45:16Z","department":[{"_id":"VlKo"}],"_id":"14084","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2023-07-10","location":"Paderborn, Germany","end_date":"2023-07-14","name":"ICALP: International Colloquium on Automata, Languages, and Programming"},"status":"public","publication_identifier":{"isbn":["9783959772785"],"issn":["1868-8969"]},"publication_status":"published","file":[{"file_name":"2023_LIPIcsICALP_Harris.pdf","date_created":"2023-08-21T06:45:16Z","file_size":917791,"date_updated":"2023-08-21T06:45:16Z","creator":"dernst","success":1,"file_id":"14088","checksum":"6dee0684245bb1c524b9c955db1e933d","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"volume":261,"abstract":[{"text":"A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We will consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n].\r\nThe partition function is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log Z(β_max))/Z(β_min)\r\nWe develop a number of algorithms to estimate the counts c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²) samples for integer-valued distributions (ignoring some second-order terms and parameters), We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs and perfect matchings in a graph.","lang":"eng"}],"oa_version":"Published Version","alternative_title":["LIPIcs"],"scopus_import":"1","month":"07","intvolume":" 261","citation":{"chicago":"Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” In 50th International Colloquium on Automata, Languages, and Programming, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.72.","ista":"Harris DG, Kolmogorov V. 2023. Parameter estimation for Gibbs distributions. 50th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LIPIcs, vol. 261, 72.","mla":"Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” 50th International Colloquium on Automata, Languages, and Programming, vol. 261, 72, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ICALP.2023.72.","ieee":"D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,” in 50th International Colloquium on Automata, Languages, and Programming, Paderborn, Germany, 2023, vol. 261.","short":"D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ama":"Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. In: 50th International Colloquium on Automata, Languages, and Programming. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.72","apa":"Harris, D. G., & Kolmogorov, V. (2023). Parameter estimation for Gibbs distributions. In 50th International Colloquium on Automata, Languages, and Programming (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.72"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Harris, David G.","last_name":"Harris","first_name":"David G."},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"}],"external_id":{"arxiv":["2007.10824"]},"article_processing_charge":"Yes","title":"Parameter estimation for Gibbs distributions","article_number":"72","has_accepted_license":"1","year":"2023","day":"01","publication":"50th International Colloquium on Automata, Languages, and Programming","doi":"10.4230/LIPIcs.ICALP.2023.72","date_published":"2023-07-01T00:00:00Z","date_created":"2023-08-20T22:01:14Z","acknowledgement":"We thank Heng Guo for helpful explanations of algorithms for sampling connected subgraphs and matchings, Maksym Serbyn for bringing to our attention the Wang-Landau algorithm and its use in physics.","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1},{"article_number":"15","external_id":{"arxiv":["2302.06420"]},"article_processing_charge":"No","author":[{"first_name":"Martin","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","last_name":"Dvorak","full_name":"Dvorak, Martin","orcid":"0000-0001-5293-214X"},{"first_name":"Jasmin","full_name":"Blanchette, Jasmin","last_name":"Blanchette"}],"title":"Closure properties of general grammars - formally verified","citation":{"ama":"Dvorak M, Blanchette J. Closure properties of general grammars - formally verified. In: 14th International Conference on Interactive Theorem Proving. Vol 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ITP.2023.15","apa":"Dvorak, M., & Blanchette, J. (2023). Closure properties of general grammars - formally verified. In 14th International Conference on Interactive Theorem Proving (Vol. 268). Bialystok, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ITP.2023.15","short":"M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ieee":"M. Dvorak and J. Blanchette, “Closure properties of general grammars - formally verified,” in 14th International Conference on Interactive Theorem Proving, Bialystok, Poland, 2023, vol. 268.","mla":"Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” 14th International Conference on Interactive Theorem Proving, vol. 268, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ITP.2023.15.","ista":"Dvorak M, Blanchette J. 2023. Closure properties of general grammars - formally verified. 14th International Conference on Interactive Theorem Proving. ITP: International Conference on Interactive Theorem Proving, LIPIcs, vol. 268, 15.","chicago":"Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” In 14th International Conference on Interactive Theorem Proving, Vol. 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ITP.2023.15."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","acknowledgement":"Jasmin Blanchette: This research has received funding from the Netherlands Organization\r\nfor Scientific Research (NWO) under the Vidi program (project No. 016.Vidi.189.037, Lean Forward).\r\n__\r\nWe thank Vladimir Kolmogorov for making this collaboration possible. We\r\nthank Václav Končický for discussing ideas about the Kleene star construction. We thank Patrick Johnson, Floris van Doorn, and Damiano Testa for their small yet very valuable contributions to our code. We thank Eric Wieser for simplifying one of our proofs. We thank Mark Summerfield for suggesting textual improvements. We thank the anonymous reviewers for very helpful comments. Finally, we thank the Lean community for helping us with various technical issues and answering many questions. ","date_created":"2023-06-05T07:29:05Z","date_published":"2023-07-27T00:00:00Z","doi":"10.4230/LIPIcs.ITP.2023.15","year":"2023","has_accepted_license":"1","publication":"14th International Conference on Interactive Theorem Proving","day":"27","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"ITP: International Conference on Interactive Theorem Proving","start_date":"2023-07-31","end_date":"2023-08-04","location":"Bialystok, Poland"},"type":"conference","status":"public","_id":"13120","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"file_date_updated":"2023-08-07T11:55:43Z","date_updated":"2023-09-25T11:04:29Z","ddc":["000"],"scopus_import":"1","alternative_title":["LIPIcs"],"intvolume":" 268","month":"07","abstract":[{"lang":"eng","text":"We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant. We defined basic notions of rewrite rules and of words derived by a grammar, and used grammars to show closure of the class of type-0 languages under four operations: union, reversal, concatenation, and the Kleene star. The literature mostly focuses on Turing machine arguments, which are possibly more difficult to formalize. For the Kleene star, we could not follow the literature and came up with our own grammar-based construction."}],"oa_version":"Published Version","related_material":{"link":[{"url":"https://github.com/madvorak/grammars/tree/publish","relation":"software"}]},"volume":268,"publication_status":"published","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959772846"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2023_LIPIcS_Dvorak.pdf","date_created":"2023-08-07T11:55:43Z","file_size":715976,"date_updated":"2023-08-07T11:55:43Z","creator":"dernst","success":1,"checksum":"773a0197f05b67feaa6cb1e17ec3642d","file_id":"13982","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}]},{"intvolume":" 2023","month":"08","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2010.09567"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in [16], [35]. As a key computational subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth convex function over a combinatorial polytope. We propose an efficient implementation of this subroutine based on in-face Frank-Wolfe directions, introduced in [4] in a different context. More generally, we define an abstract data structure for a combinatorial subproblem that enables in-face FW directions, and describe its specialization for tree-structured MAP-MRF inference subproblems. Experimental results indicate that the resulting method is the current state-of-art LP solver for some classes of problems. Our code is available at pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html."}],"volume":2023,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["9798350301298"],"issn":["1063-6919"]},"status":"public","conference":{"name":"CVPR: Conference on Computer Vision and Pattern Recognition","end_date":"2023-06-24","location":"Vancouver, Canada","start_date":"2023-06-17"},"type":"conference","_id":"14448","department":[{"_id":"VlKo"}],"date_updated":"2023-10-31T12:01:24Z","oa":1,"quality_controlled":"1","publisher":"IEEE","date_created":"2023-10-22T22:01:16Z","doi":"10.1109/CVPR52729.2023.01153","date_published":"2023-08-22T00:00:00Z","page":"11980-11989","publication":"Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition","day":"22","year":"2023","title":"Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions","article_processing_charge":"No","external_id":{"arxiv":["2010.09567"]},"author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Kolmogorov, V. (2023). Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 2023, pp. 11980–11989). Vancouver, Canada: IEEE. https://doi.org/10.1109/CVPR52729.2023.01153","ama":"Kolmogorov V. Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol 2023. IEEE; 2023:11980-11989. doi:10.1109/CVPR52729.2023.01153","ieee":"V. Kolmogorov, “Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vancouver, Canada, 2023, vol. 2023, pp. 11980–11989.","short":"V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2023, pp. 11980–11989.","mla":"Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial in-Face Frank-Wolfe Directions.” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2023, IEEE, 2023, pp. 11980–89, doi:10.1109/CVPR52729.2023.01153.","ista":"Kolmogorov V. 2023. Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition vol. 2023, 11980–11989.","chicago":"Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial in-Face Frank-Wolfe Directions.” In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2023:11980–89. IEEE, 2023. https://doi.org/10.1109/CVPR52729.2023.01153."}},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Takhanov R, Kolmogorov V. 2022. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 26(1), 257–272.","chicago":"Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and Weighted Context-Free Grammars.” Intelligent Data Analysis. IOS Press, 2022. https://doi.org/10.3233/IDA-205623.","ieee":"R. Takhanov and V. Kolmogorov, “Combining pattern-based CRFs and weighted context-free grammars,” Intelligent Data Analysis, vol. 26, no. 1. IOS Press, pp. 257–272, 2022.","short":"R. Takhanov, V. Kolmogorov, Intelligent Data Analysis 26 (2022) 257–272.","apa":"Takhanov, R., & Kolmogorov, V. (2022). Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. IOS Press. https://doi.org/10.3233/IDA-205623","ama":"Takhanov R, Kolmogorov V. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 2022;26(1):257-272. doi:10.3233/IDA-205623","mla":"Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and Weighted Context-Free Grammars.” Intelligent Data Analysis, vol. 26, no. 1, IOS Press, 2022, pp. 257–72, doi:10.3233/IDA-205623."},"title":"Combining pattern-based CRFs and weighted context-free grammars","author":[{"last_name":"Takhanov","full_name":"Takhanov, Rustem","first_name":"Rustem","id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"}],"article_processing_charge":"No","external_id":{"isi":["000749997700015"],"arxiv":["1404.5475"]},"quality_controlled":"1","publisher":"IOS Press","oa":1,"day":"14","publication":"Intelligent Data Analysis","isi":1,"year":"2022","date_published":"2022-01-14T00:00:00Z","doi":"10.3233/IDA-205623","date_created":"2022-02-06T23:01:32Z","page":"257-272","_id":"10737","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-08-02T14:09:41Z","department":[{"_id":"VlKo"}],"oa_version":"Preprint","abstract":[{"text":"We consider two models for the sequence labeling (tagging) problem. The first one is a Pattern-Based Conditional Random Field (PB), in which the energy of a string (chain labeling) x=x1…xn∈Dn is a sum of terms over intervals [i,j] where each term is non-zero only if the substring xi…xj equals a prespecified word w∈Λ. The second model is a Weighted Context-Free Grammar (WCFG) frequently used for natural language processing. PB and WCFG encode local and non-local interactions respectively, and thus can be viewed as complementary. We propose a Grammatical Pattern-Based CRF model (GPB) that combines the two in a natural way. We argue that it has certain advantages over existing approaches such as the Hybrid model of Benedí and Sanchez that combines N-grams and WCFGs. The focus of this paper is to analyze the complexity of inference tasks in a GPB such as computing MAP. We present a polynomial-time algorithm for general GPBs and a faster version for a special case that we call Interaction Grammars.","lang":"eng"}],"month":"01","intvolume":" 26","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1404.5475"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1088-467X"],"eissn":["1571-4128"]},"publication_status":"published","issue":"1","volume":26},{"_id":"7577","article_type":"original","type":"journal_article","status":"public","date_updated":"2024-03-05T14:01:52Z","ddc":["510","515","518"],"department":[{"_id":"VlKo"}],"file_date_updated":"2021-03-16T23:30:06Z","abstract":[{"lang":"eng","text":"Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods."}],"oa_version":"Submitted Version","scopus_import":"1","month":"01","intvolume":" 101","publication_identifier":{"eissn":["1563-504X"],"issn":["0003-6811"]},"publication_status":"published","file":[{"checksum":"869efe8cb09505dfa6012f67d20db63d","file_id":"8648","embargo":"2021-03-15","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2020-10-12T10:42:54Z","file_name":"2020_ApplicAnalysis_Shehu.pdf","creator":"dernst","date_updated":"2021-03-16T23:30:06Z","file_size":4282586}],"language":[{"iso":"eng"}],"issue":"1","volume":101,"ec_funded":1,"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"citation":{"mla":"Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor & Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287.","ama":"Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287","apa":"Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287","ieee":"Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor & Francis, pp. 192–216, 2022.","short":"Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216.","chicago":"Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor & Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287.","ista":"Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Shehu","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Iyiola","full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S."}],"external_id":{"arxiv":["2101.08057"],"isi":["000518364100001"]},"article_processing_charge":"No","title":"Weak convergence for variational inequalities with inertial-type method","acknowledgement":"The project of the first author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160).","quality_controlled":"1","publisher":"Taylor & Francis","oa":1,"isi":1,"has_accepted_license":"1","year":"2022","day":"01","publication":"Applicable Analysis","page":"192-216","date_published":"2022-01-01T00:00:00Z","doi":"10.1080/00036811.2020.1736287","date_created":"2020-03-09T07:06:52Z"},{"oa":1,"publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","quality_controlled":"1","acknowledgement":"Fotis Iliopoulos: This material is based upon work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the National Science Foundation Grant No. CCF-1815328.\r\nVladimir Kolmogorov: Supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160.","date_created":"2021-10-03T22:01:22Z","date_published":"2021-09-15T00:00:00Z","doi":"10.4230/LIPIcs.APPROX/RANDOM.2021.31","year":"2021","has_accepted_license":"1","publication":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques","day":"15","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"article_number":"31","external_id":{"arxiv":["2008.05569"]},"article_processing_charge":"Yes","author":[{"full_name":"Harris, David G.","last_name":"Harris","first_name":"David G."},{"last_name":"Iliopoulos","full_name":"Iliopoulos, Fotis","first_name":"Fotis"},{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"}],"title":"A new notion of commutativity for the algorithmic Lovász Local Lemma","citation":{"mla":"Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, vol. 207, 31, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31.","ieee":"D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity for the algorithmic Lovász Local Lemma,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Virtual, 2021, vol. 207.","short":"D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","ama":"Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the algorithmic Lovász Local Lemma. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Vol 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31","apa":"Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2021). A new notion of commutativity for the algorithmic Lovász Local Lemma. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Vol. 207). Virtual: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31","chicago":"Harris, David G., Fotis Iliopoulos, and Vladimir Kolmogorov. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Vol. 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31.","ista":"Harris DG, Iliopoulos F, Kolmogorov V. 2021. A new notion of commutativity for the algorithmic Lovász Local Lemma. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation, LIPIcs, vol. 207, 31."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","alternative_title":["LIPIcs"],"intvolume":" 207","month":"09","abstract":[{"lang":"eng","text":"The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works revealed that the LLL has intimate connections with a class of stochastic local search algorithms for finding such desirable objects. In particular, it can be seen as a sufficient condition for this type of algorithms to converge fast. Besides conditions for existence of and fast convergence to desirable objects, one may naturally ask further questions regarding properties of these algorithms. For instance, \"are they parallelizable?\", \"how many solutions can they output?\", \"what is the expected \"weight\" of a solution?\", etc. These questions and more have been answered for a class of LLL-inspired algorithms called commutative. In this paper we introduce a new, very natural and more general notion of commutativity (essentially matrix commutativity) which allows us to show a number of new refined properties of LLL-inspired local search algorithms with significantly simpler proofs."}],"oa_version":"Published Version","ec_funded":1,"volume":207,"publication_status":"published","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-9597-7207-5"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"9d2544d53aa5b01565c6891d97a4d765","file_id":"10098","success":1,"date_updated":"2021-10-06T13:51:54Z","file_size":804472,"creator":"cchlebak","date_created":"2021-10-06T13:51:54Z","file_name":"2021_LIPIcs_Harris.pdf"}],"conference":{"name":"APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation","start_date":"2021-08-16","location":"Virtual","end_date":"2021-08-18"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","status":"public","_id":"10072","department":[{"_id":"VlKo"}],"file_date_updated":"2021-10-06T13:51:54Z","date_updated":"2022-03-18T10:08:25Z","ddc":["000"]},{"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"status":"public","conference":{"start_date":"2021-07-18","end_date":"2021-07-24","location":"Virtual","name":"ICML: International Conference on Machine Learning"},"type":"conference","_id":"10552","title":"One-sided Frank-Wolfe algorithms for saddle problems","department":[{"_id":"VlKo"}],"article_processing_charge":"No","external_id":{"arxiv":["2101.12617"]},"author":[{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"first_name":"Thomas","last_name":"Pock","full_name":"Pock, Thomas"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ista":"Kolmogorov V, Pock T. 2021. One-sided Frank-Wolfe algorithms for saddle problems. 38th International Conference on Machine Learning. ICML: International Conference on Machine Learning.","chicago":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” In 38th International Conference on Machine Learning, 2021.","ieee":"V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,” in 38th International Conference on Machine Learning, Virtual, 2021.","short":"V. Kolmogorov, T. Pock, in:, 38th International Conference on Machine Learning, 2021.","apa":"Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for saddle problems. In 38th International Conference on Machine Learning. Virtual.","ama":"Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems. In: 38th International Conference on Machine Learning. ; 2021.","mla":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” 38th International Conference on Machine Learning, 2021."},"date_updated":"2021-12-17T09:06:46Z","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/2101.12617","open_access":"1"}],"oa":1,"quality_controlled":"1","acknowledgement":"Vladimir Kolmogorov was supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160. Thomas Pock acknowledges support by an ERC grant HOMOVIS, no 640156.","oa_version":"Preprint","abstract":[{"text":"We study a class of convex-concave saddle-point problems of the form minxmaxy⟨Kx,y⟩+fP(x)−h∗(y) where K is a linear operator, fP is the sum of a convex function f with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope P, and h∗ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle (lmo) for fP and an efficient proximal map for h∗ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case h∗ is the indicator function of a linear constraint and function f is quadratic, we show a O(1/n2) convergence rate on the dual objective, requiring O(nlogn) calls of lmo. If the problem comes from the constrained optimization problem minx∈Rd{fP(x)|Ax−b=0} then we additionally get bound O(1/n2) both on the primal gap and on the infeasibility gap. In the most general case, we show a O(1/n) convergence rate of the primal-dual gap again requiring O(nlogn) calls of lmo. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision.","lang":"eng"}],"ec_funded":1,"date_created":"2021-12-16T12:41:20Z","date_published":"2021-07-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"38th International Conference on Machine Learning","day":"01","publication_status":"published","year":"2021"},{"title":"Massively winning configurations in the convex grabbing game on the plane","article_processing_charge":"No","external_id":{"arxiv":["2106.11247"]},"author":[{"first_name":"Martin","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","last_name":"Dvorak","orcid":"0000-0001-5293-214X","full_name":"Dvorak, Martin"},{"first_name":"Sara","full_name":"Nicholson, Sara","last_name":"Nicholson"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. Proceedings of the 33rd Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry.","chicago":"Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” In Proceedings of the 33rd Canadian Conference on Computational Geometry, n.d.","short":"M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference on Computational Geometry, n.d.","ieee":"M. Dvorak and S. Nicholson, “Massively winning configurations in the convex grabbing game on the plane,” in Proceedings of the 33rd Canadian Conference on Computational Geometry, Halifax, NS, Canada.","apa":"Dvorak, M., & Nicholson, S. (n.d.). Massively winning configurations in the convex grabbing game on the plane. In Proceedings of the 33rd Canadian Conference on Computational Geometry. Halifax, NS, Canada.","ama":"Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. In: Proceedings of the 33rd Canadian Conference on Computational Geometry.","mla":"Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” Proceedings of the 33rd Canadian Conference on Computational Geometry."},"date_created":"2021-06-22T15:57:11Z","date_published":"2021-06-29T00:00:00Z","publication":"Proceedings of the 33rd Canadian Conference on Computational Geometry","day":"29","year":"2021","has_accepted_license":"1","oa":1,"quality_controlled":"1","file_date_updated":"2021-08-12T10:57:21Z","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"ddc":["516"],"date_updated":"2021-08-12T10:57:39Z","keyword":["convex grabbing game","graph grabbing game","combinatorial game","convex geometry"],"status":"public","conference":{"start_date":"2021-08-10","location":"Halifax, NS, Canada","end_date":"2021-08-12","name":"CCCG: Canadian Conference on Computational Geometry"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"type":"conference","_id":"9592","license":"https://creativecommons.org/licenses/by-nd/4.0/","language":[{"iso":"eng"}],"file":[{"date_created":"2021-06-28T20:23:13Z","file_name":"Convex-Grabbing-Game_CCCG_proc_version.pdf","creator":"mdvorak","date_updated":"2021-06-28T20:23:13Z","file_size":381306,"file_id":"9616","checksum":"45accb1de9b7e0e4bb2fbfe5fd3e6239","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"},{"file_name":"Convex-Grabbing-Game_FULL-VERSION.pdf","date_created":"2021-08-12T10:57:21Z","creator":"kschuh","file_size":403645,"date_updated":"2021-08-12T10:57:21Z","success":1,"file_id":"9902","checksum":"9199cf18c65658553487458cc24d0ab2","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"publication_status":"accepted","month":"06","oa_version":"Submitted Version","abstract":[{"text":"The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large odd-sized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large even-sized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general.","lang":"eng"}]},{"author":[{"last_name":"Iyiola","full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S."},{"last_name":"Enyi","full_name":"Enyi, Cyril D.","first_name":"Cyril D."},{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","last_name":"Shehu"}],"external_id":{"isi":["000650507600001"]},"article_processing_charge":"No","title":"Reflected three-operator splitting method for monotone inclusion problem","citation":{"mla":"Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software, Taylor and Francis, 2021, doi:10.1080/10556788.2021.1924715.","ama":"Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 2021. doi:10.1080/10556788.2021.1924715","apa":"Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2021). Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. Taylor and Francis. https://doi.org/10.1080/10556788.2021.1924715","ieee":"O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” Optimization Methods and Software. Taylor and Francis, 2021.","short":"O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software (2021).","chicago":"Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software. Taylor and Francis, 2021. https://doi.org/10.1080/10556788.2021.1924715.","ista":"Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"doi":"10.1080/10556788.2021.1924715","date_published":"2021-05-12T00:00:00Z","date_created":"2021-06-06T22:01:30Z","isi":1,"year":"2021","day":"12","publication":"Optimization Methods and Software","publisher":"Taylor and Francis","quality_controlled":"1","acknowledgement":"The authors are grateful to the anonymous referees and the handling Editor for their insightful comments which have improved the earlier version of the manuscript greatly. The second author is grateful to the University of Hafr Al Batin. The last author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160).","department":[{"_id":"VlKo"}],"date_updated":"2023-08-08T13:57:43Z","article_type":"original","type":"journal_article","status":"public","_id":"9469","ec_funded":1,"publication_identifier":{"eissn":["1029-4937"],"issn":["1055-6788"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","month":"05","abstract":[{"lang":"eng","text":"In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis."}],"oa_version":"None"},{"publication_identifier":{"eissn":["1572-9427"],"issn":["1566-113X"]},"publication_status":"published","file":[{"date_created":"2021-08-11T12:44:16Z","file_name":"2021_NetworksSpatialEconomics_Shehu.pdf","date_updated":"2021-08-11T12:44:16Z","file_size":834964,"creator":"kschuh","file_id":"9884","checksum":"22b4253a2e5da843622a2df713784b4c","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"issue":"2","volume":21,"ec_funded":1,"abstract":[{"text":"In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"06","intvolume":" 21","date_updated":"2023-09-05T15:32:32Z","ddc":["510"],"file_date_updated":"2021-08-11T12:44:16Z","department":[{"_id":"VlKo"}],"_id":"9234","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Computer Networks and Communications","Software","Artificial Intelligence"],"isi":1,"has_accepted_license":"1","year":"2021","day":"01","publication":"Networks and Spatial Economics","page":"291-323","doi":"10.1007/s11067-021-09517-w","date_published":"2021-06-01T00:00:00Z","date_created":"2021-03-10T12:18:47Z","acknowledgement":"The authors sincerely thank the Editor-in-Chief and anonymous referees for their careful reading, constructive comments and fruitful suggestions that help improve the manuscript. The research of the first author is supported by the National Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral Fellowship; Grant Number: 120784). The first author also acknowledges the financial support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Postdoctoral Fellowship. The second author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). Open Access funding provided by Institute of Science and Technology (IST Austria).","quality_controlled":"1","publisher":"Springer Nature","oa":1,"citation":{"ieee":"C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity,” Networks and Spatial Economics, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021.","short":"C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323.","apa":"Izuchukwu, C., & Shehu, Y. (2021). New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. Springer Nature. https://doi.org/10.1007/s11067-021-09517-w","ama":"Izuchukwu C, Shehu Y. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. 2021;21(2):291-323. doi:10.1007/s11067-021-09517-w","mla":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks and Spatial Economics, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323, doi:10.1007/s11067-021-09517-w.","ista":"Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. 21(2), 291–323.","chicago":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks and Spatial Economics. Springer Nature, 2021. https://doi.org/10.1007/s11067-021-09517-w."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"full_name":"Izuchukwu, Chinedu","last_name":"Izuchukwu","first_name":"Chinedu"},{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","last_name":"Shehu","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000625002100001"]},"title":"New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity","project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-10-10T09:29:08Z","citation":{"mla":"Bloch-Hansen, Andrew, et al. “Experimental Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem.” Conference on Algorithms and Discrete Applied Mathematics, vol. 12601, Springer Nature, 2021, pp. 346–58, doi:10.1007/978-3-030-67899-9_28.","short":"A. Bloch-Hansen, N. Samei, R. Solis-Oba, in:, Conference on Algorithms and Discrete Applied Mathematics, Springer Nature, 2021, pp. 346–358.","ieee":"A. Bloch-Hansen, N. Samei, and R. Solis-Oba, “Experimental evaluation of a local search approximation algorithm for the multiway cut problem,” in Conference on Algorithms and Discrete Applied Mathematics, Rupnagar, India, 2021, vol. 12601, pp. 346–358.","apa":"Bloch-Hansen, A., Samei, N., & Solis-Oba, R. (2021). Experimental evaluation of a local search approximation algorithm for the multiway cut problem. In Conference on Algorithms and Discrete Applied Mathematics (Vol. 12601, pp. 346–358). Rupnagar, India: Springer Nature. https://doi.org/10.1007/978-3-030-67899-9_28","ama":"Bloch-Hansen A, Samei N, Solis-Oba R. Experimental evaluation of a local search approximation algorithm for the multiway cut problem. In: Conference on Algorithms and Discrete Applied Mathematics. Vol 12601. Springer Nature; 2021:346-358. doi:10.1007/978-3-030-67899-9_28","chicago":"Bloch-Hansen, Andrew, Nasim Samei, and Roberto Solis-Oba. “Experimental Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem.” In Conference on Algorithms and Discrete Applied Mathematics, 12601:346–58. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-67899-9_28.","ista":"Bloch-Hansen A, Samei N, Solis-Oba R. 2021. Experimental evaluation of a local search approximation algorithm for the multiway cut problem. Conference on Algorithms and Discrete Applied Mathematics. CALDAM: Conference on Algorithms and Discrete Applied Mathematics, LNCS, vol. 12601, 346–358."},"title":"Experimental evaluation of a local search approximation algorithm for the multiway cut problem","department":[{"_id":"VlKo"}],"author":[{"first_name":"Andrew","full_name":"Bloch-Hansen, Andrew","last_name":"Bloch-Hansen"},{"first_name":"Nasim","id":"C1531CAE-36E9-11EA-845F-33AA3DDC885E","last_name":"Samei","full_name":"Samei, Nasim"},{"first_name":"Roberto","last_name":"Solis-Oba","full_name":"Solis-Oba, Roberto"}],"article_processing_charge":"No","_id":"9227","status":"public","type":"conference","conference":{"name":"CALDAM: Conference on Algorithms and Discrete Applied Mathematics","start_date":"2021-02-11","end_date":"2021-02-13","location":"Rupnagar, India"},"day":"28","publication":"Conference on Algorithms and Discrete Applied Mathematics","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030678982"],"issn":["0302-9743"]},"publication_status":"published","year":"2021","volume":12601,"date_published":"2021-01-28T00:00:00Z","doi":"10.1007/978-3-030-67899-9_28","date_created":"2021-03-07T23:01:25Z","page":"346-358","oa_version":"None","abstract":[{"lang":"eng","text":"In the multiway cut problem we are given a weighted undirected graph G=(V,E) and a set T⊆V of k terminals. The goal is to find a minimum weight set of edges E′⊆E with the property that by removing E′ from G all the terminals become disconnected. In this paper we present a simple local search approximation algorithm for the multiway cut problem with approximation ratio 2−2k . We present an experimental evaluation of the performance of our local search algorithm and show that it greatly outperforms the isolation heuristic of Dalhaus et al. and it has similar performance as the much more complex algorithms of Calinescu et al., Sharma and Vondrak, and Buchbinder et al. which have the currently best known approximation ratios for this problem."}],"month":"01","intvolume":" 12601","quality_controlled":"1","publisher":"Springer Nature","scopus_import":"1","alternative_title":["LNCS"]},{"department":[{"_id":"VlKo"}],"date_updated":"2023-10-10T09:30:23Z","status":"public","article_type":"original","type":"journal_article","_id":"8817","volume":93,"issue":"2","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1432-2994"],"eissn":["1432-5217"]},"publication_status":"published","month":"04","intvolume":" 93","scopus_import":"1","oa_version":"None","abstract":[{"text":"The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model.","lang":"eng"}],"title":"An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems","author":[{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu"},{"full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola","first_name":"Olaniyi S."},{"last_name":"Thong","full_name":"Thong, Duong Viet","first_name":"Duong Viet"},{"last_name":"Van","full_name":"Van, Nguyen Thi Cam","first_name":"Nguyen Thi Cam"}],"article_processing_charge":"No","external_id":{"isi":["000590497300001"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Shehu, Yekini, Olaniyi S. Iyiola, Duong Viet Thong, and Nguyen Thi Cam Van. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research. Springer Nature, 2021. https://doi.org/10.1007/s00186-020-00730-w.","ista":"Shehu Y, Iyiola OS, Thong DV, Van NTC. 2021. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 93(2), 213–242.","mla":"Shehu, Yekini, et al. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research, vol. 93, no. 2, Springer Nature, 2021, pp. 213–42, doi:10.1007/s00186-020-00730-w.","short":"Y. Shehu, O.S. Iyiola, D.V. Thong, N.T.C. Van, Mathematical Methods of Operations Research 93 (2021) 213–242.","ieee":"Y. Shehu, O. S. Iyiola, D. V. Thong, and N. T. C. Van, “An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems,” Mathematical Methods of Operations Research, vol. 93, no. 2. Springer Nature, pp. 213–242, 2021.","ama":"Shehu Y, Iyiola OS, Thong DV, Van NTC. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 2021;93(2):213-242. doi:10.1007/s00186-020-00730-w","apa":"Shehu, Y., Iyiola, O. S., Thong, D. V., & Van, N. T. C. (2021). An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. Springer Nature. https://doi.org/10.1007/s00186-020-00730-w"},"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_published":"2021-04-01T00:00:00Z","doi":"10.1007/s00186-020-00730-w","date_created":"2020-11-29T23:01:18Z","page":"213-242","day":"01","publication":"Mathematical Methods of Operations Research","isi":1,"year":"2021","publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The authors are grateful to the two referees and the Associate Editor for their comments and suggestions which have improved the earlier version of the paper greatly. The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160)."},{"date_created":"2021-04-11T22:01:14Z","doi":"10.1007/s00025-021-01381-x","date_published":"2021-03-25T00:00:00Z","year":"2021","isi":1,"publication":"Results in Mathematics","day":"25","publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria.","article_processing_charge":"No","external_id":{"isi":["000632917700001"]},"author":[{"first_name":"Olaniyi S.","full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola"},{"orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"}],"title":"New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications","citation":{"ista":"Iyiola OS, Shehu Y. 2021. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 76(2), 75.","chicago":"Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results in Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s00025-021-01381-x.","ama":"Iyiola OS, Shehu Y. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 2021;76(2). doi:10.1007/s00025-021-01381-x","apa":"Iyiola, O. S., & Shehu, Y. (2021). New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. Springer Nature. https://doi.org/10.1007/s00025-021-01381-x","ieee":"O. S. Iyiola and Y. Shehu, “New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications,” Results in Mathematics, vol. 76, no. 2. Springer Nature, 2021.","short":"O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021).","mla":"Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results in Mathematics, vol. 76, no. 2, 75, Springer Nature, 2021, doi:10.1007/s00025-021-01381-x."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"75","issue":"2","volume":76,"publication_status":"published","publication_identifier":{"issn":["1422-6383"],"eissn":["1420-9012"]},"language":[{"iso":"eng"}],"scopus_import":"1","intvolume":" 76","month":"03","abstract":[{"lang":"eng","text":"We consider inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. To do these, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators in infinite dimensional real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature. We then show that Fermat–Weber location problem and primal–dual three-operator splitting are special cases of fixed point problem of nonexpansive mapping and consequently obtain the convergence analysis of inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. Some numerical implementations are drawn from primal–dual three-operator splitting to support the theoretical analysis."}],"oa_version":"None","department":[{"_id":"VlKo"}],"date_updated":"2023-10-10T09:47:33Z","type":"journal_article","article_type":"original","status":"public","_id":"9315"},{"acknowledgement":"The second author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160).","quality_controlled":"1","publisher":"Taylor and Francis","day":"14","publication":"Optimization","isi":1,"year":"2021","doi":"10.1080/02331934.2021.1914035","date_published":"2021-04-14T00:00:00Z","date_created":"2021-05-02T22:01:29Z","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Ogbuisi, Ferdinard U., Yekini Shehu, and Jen Chih Yao. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization. Taylor and Francis, 2021. https://doi.org/10.1080/02331934.2021.1914035.","ista":"Ogbuisi FU, Shehu Y, Yao JC. 2021. Convergence analysis of new inertial method for the split common null point problem. Optimization.","mla":"Ogbuisi, Ferdinard U., et al. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization, Taylor and Francis, 2021, doi:10.1080/02331934.2021.1914035.","ieee":"F. U. Ogbuisi, Y. Shehu, and J. C. Yao, “Convergence analysis of new inertial method for the split common null point problem,” Optimization. Taylor and Francis, 2021.","short":"F.U. Ogbuisi, Y. Shehu, J.C. Yao, Optimization (2021).","apa":"Ogbuisi, F. U., Shehu, Y., & Yao, J. C. (2021). Convergence analysis of new inertial method for the split common null point problem. Optimization. Taylor and Francis. https://doi.org/10.1080/02331934.2021.1914035","ama":"Ogbuisi FU, Shehu Y, Yao JC. Convergence analysis of new inertial method for the split common null point problem. Optimization. 2021. doi:10.1080/02331934.2021.1914035"},"title":"Convergence analysis of new inertial method for the split common null point problem","author":[{"last_name":"Ogbuisi","full_name":"Ogbuisi, Ferdinard U.","first_name":"Ferdinard U."},{"last_name":"Shehu","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"},{"full_name":"Yao, Jen Chih","last_name":"Yao","first_name":"Jen Chih"}],"article_processing_charge":"No","external_id":{"isi":["000640109300001"]},"oa_version":"None","abstract":[{"lang":"eng","text":"In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method."}],"month":"04","scopus_import":"1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1029-4945"],"issn":["0233-1934"]},"publication_status":"published","ec_funded":1,"_id":"9365","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-10-10T09:48:41Z","department":[{"_id":"VlKo"}]},{"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"8196","department":[{"_id":"VlKo"}],"file_date_updated":"2020-08-03T15:24:39Z","ddc":["510"],"date_updated":"2024-03-07T14:39:29Z","intvolume":" 22","month":"02","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis."}],"ec_funded":1,"volume":22,"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":2137860,"date_updated":"2020-08-03T15:24:39Z","file_name":"2020_OptimizationEngineering_Shehu.pdf","date_created":"2020-08-03T15:24:39Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"8197"}],"publication_status":"published","publication_identifier":{"issn":["1389-4420"],"eissn":["1573-2924"]},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"title":"New strong convergence method for the sum of two maximal monotone operators","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000559345400001"]},"author":[{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"},{"last_name":"Dong","full_name":"Dong, Qiao-Li","first_name":"Qiao-Li"},{"last_name":"Liu","full_name":"Liu, Lu-Lu","first_name":"Lu-Lu"},{"first_name":"Jen-Chih","last_name":"Yao","full_name":"Yao, Jen-Chih"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Shehu, Yekini, Qiao-Li Dong, Lu-Lu Liu, and Jen-Chih Yao. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering. Springer Nature, 2021. https://doi.org/10.1007/s11081-020-09544-5.","ista":"Shehu Y, Dong Q-L, Liu L-L, Yao J-C. 2021. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 22, 2627–2653.","mla":"Shehu, Yekini, et al. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering, vol. 22, Springer Nature, 2021, pp. 2627–53, doi:10.1007/s11081-020-09544-5.","ama":"Shehu Y, Dong Q-L, Liu L-L, Yao J-C. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 2021;22:2627-2653. doi:10.1007/s11081-020-09544-5","apa":"Shehu, Y., Dong, Q.-L., Liu, L.-L., & Yao, J.-C. (2021). New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. Springer Nature. https://doi.org/10.1007/s11081-020-09544-5","short":"Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering 22 (2021) 2627–2653.","ieee":"Y. Shehu, Q.-L. Dong, L.-L. Liu, and J.-C. Yao, “New strong convergence method for the sum of two maximal monotone operators,” Optimization and Engineering, vol. 22. Springer Nature, pp. 2627–2653, 2021."},"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7—2007–2013) (Grant Agreement No. 616160). The authors are grateful to the anonymous referees and the handling Editor for their comments and suggestions which have improved the earlier version of the manuscript greatly.","date_created":"2020-08-03T14:29:57Z","doi":"10.1007/s11081-020-09544-5","date_published":"2021-02-25T00:00:00Z","page":"2627-2653","publication":"Optimization and Engineering","day":"25","year":"2021","isi":1,"has_accepted_license":"1"},{"month":"09","intvolume":" 15","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.","lang":"eng"}],"volume":15,"ec_funded":1,"file":[{"file_name":"2021_OptimizationLetters_Shehu.pdf","date_created":"2024-03-07T14:58:51Z","creator":"kschuh","file_size":2148882,"date_updated":"2024-03-07T14:58:51Z","success":1,"checksum":"63c5f31cd04626152a19f97a2476281b","file_id":"15089","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1862-4472"],"eissn":["1862-4480"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"7925","department":[{"_id":"VlKo"}],"file_date_updated":"2024-03-07T14:58:51Z","ddc":["510"],"date_updated":"2024-03-07T15:00:43Z","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are grateful to the referees for their insightful comments which have improved the earlier version of the manuscript greatly. The first author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160).","doi":"10.1007/s11590-020-01603-1","date_published":"2021-09-01T00:00:00Z","date_created":"2020-06-04T11:28:33Z","page":"2109-2126","day":"01","publication":"Optimization Letters","isi":1,"has_accepted_license":"1","year":"2021","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"title":"New inertial relaxed method for solving split feasibilities","author":[{"last_name":"Shehu","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"},{"first_name":"Aviv","full_name":"Gibali, Aviv","last_name":"Gibali"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000537342300001"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters, vol. 15, Springer Nature, 2021, pp. 2109–26, doi:10.1007/s11590-020-01603-1.","ieee":"Y. Shehu and A. Gibali, “New inertial relaxed method for solving split feasibilities,” Optimization Letters, vol. 15. Springer Nature, pp. 2109–2126, 2021.","short":"Y. Shehu, A. Gibali, Optimization Letters 15 (2021) 2109–2126.","apa":"Shehu, Y., & Gibali, A. (2021). New inertial relaxed method for solving split feasibilities. Optimization Letters. Springer Nature. https://doi.org/10.1007/s11590-020-01603-1","ama":"Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities. Optimization Letters. 2021;15:2109-2126. doi:10.1007/s11590-020-01603-1","chicago":"Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters. Springer Nature, 2021. https://doi.org/10.1007/s11590-020-01603-1.","ista":"Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities. Optimization Letters. 15, 2109–2126."}},{"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"author":[{"last_name":"Shehu","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Li, Xiao-Huan","last_name":"Li","first_name":"Xiao-Huan"},{"first_name":"Qiao-Li","full_name":"Dong, Qiao-Li","last_name":"Dong"}],"article_processing_charge":"No","external_id":{"isi":["000528979000015"]},"title":"An efficient projection-type method for monotone variational inequalities in Hilbert spaces","citation":{"mla":"Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms, vol. 84, Springer Nature, 2020, pp. 365–88, doi:10.1007/s11075-019-00758-y.","ieee":"Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for monotone variational inequalities in Hilbert spaces,” Numerical Algorithms, vol. 84. Springer Nature, pp. 365–388, 2020.","short":"Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.","ama":"Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 2020;84:365-388. doi:10.1007/s11075-019-00758-y","apa":"Shehu, Y., Li, X.-H., & Dong, Q.-L. (2020). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. Springer Nature. https://doi.org/10.1007/s11075-019-00758-y","chicago":"Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms. Springer Nature, 2020. https://doi.org/10.1007/s11075-019-00758-y.","ista":"Shehu Y, Li X-H, Dong Q-L. 2020. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 84, 365–388."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"The research of this author is supported by the ERC grant at the IST.","page":"365-388","date_published":"2020-05-01T00:00:00Z","doi":"10.1007/s11075-019-00758-y","date_created":"2019-06-27T20:09:33Z","isi":1,"has_accepted_license":"1","year":"2020","day":"01","publication":"Numerical Algorithms","article_type":"original","type":"journal_article","status":"public","_id":"6593","department":[{"_id":"VlKo"}],"file_date_updated":"2020-07-14T12:47:34Z","date_updated":"2023-08-17T13:51:18Z","ddc":["000"],"scopus_import":"1","month":"05","intvolume":" 84","abstract":[{"text":"We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.","lang":"eng"}],"oa_version":"Submitted Version","volume":84,"ec_funded":1,"publication_identifier":{"issn":["1017-1398"],"eissn":["1572-9265"]},"publication_status":"published","file":[{"checksum":"bb1a1eb3ebb2df380863d0db594673ba","file_id":"6927","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-10-01T13:14:10Z","file_name":"ExtragradientMethodPaper.pdf","creator":"kschuh","date_updated":"2020-07-14T12:47:34Z","file_size":359654}],"language":[{"iso":"eng"}]},{"author":[{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Olaniyi S.","full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola"}],"external_id":{"isi":["000564648400018"]},"article_processing_charge":"No","title":"Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence","citation":{"apa":"Shehu, Y., & Iyiola, O. S. (2020). Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2020.06.009","ama":"Shehu Y, Iyiola OS. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. 2020;157:315-337. doi:10.1016/j.apnum.2020.06.009","short":"Y. Shehu, O.S. Iyiola, Applied Numerical Mathematics 157 (2020) 315–337.","ieee":"Y. Shehu and O. S. Iyiola, “Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence,” Applied Numerical Mathematics, vol. 157. Elsevier, pp. 315–337, 2020.","mla":"Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” Applied Numerical Mathematics, vol. 157, Elsevier, 2020, pp. 315–37, doi:10.1016/j.apnum.2020.06.009.","ista":"Shehu Y, Iyiola OS. 2020. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. 157, 315–337.","chicago":"Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” Applied Numerical Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.apnum.2020.06.009."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"page":"315-337","doi":"10.1016/j.apnum.2020.06.009","date_published":"2020-11-01T00:00:00Z","date_created":"2020-07-02T09:02:33Z","has_accepted_license":"1","isi":1,"year":"2020","day":"01","publication":"Applied Numerical Mathematics","quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"The authors are grateful to the two anonymous referees for their insightful comments and suggestions which have improved the earlier version of the manuscript greatly. The first author has received funding from the European Research Council (ERC) under the European Union Seventh Framework Programme (FP7 - 2007-2013) (Grant agreement No. 616160).","department":[{"_id":"VlKo"}],"file_date_updated":"2020-07-14T12:48:09Z","date_updated":"2023-08-22T07:50:43Z","ddc":["510"],"article_type":"original","type":"journal_article","status":"public","_id":"8077","volume":157,"ec_funded":1,"publication_identifier":{"issn":["0168-9274"]},"publication_status":"published","file":[{"checksum":"87d81324a62c82baa925c009dfcb0200","file_id":"8078","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2020-07-02T09:08:59Z","file_name":"2020_AppliedNumericalMath_Shehu.pdf","creator":"dernst","date_updated":"2020-07-14T12:48:09Z","file_size":2874203}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"11","intvolume":" 157","abstract":[{"lang":"eng","text":"The projection methods with vanilla inertial extrapolation step for variational inequalities have been of interest to many authors recently due to the improved convergence speed contributed by the presence of inertial extrapolation step. However, it is discovered that these projection methods with inertial steps lose the Fejér monotonicity of the iterates with respect to the solution, which is being enjoyed by their corresponding non-inertial projection methods for variational inequalities. This lack of Fejér monotonicity makes projection methods with vanilla inertial extrapolation step for variational inequalities not to converge faster than their corresponding non-inertial projection methods at times. Also, it has recently been proved that the projection methods with vanilla inertial extrapolation step may provide convergence rates that are worse than the classical projected gradient methods for strongly convex functions. In this paper, we introduce projection methods with alternated inertial extrapolation step for solving variational inequalities. We show that the sequence of iterates generated by our methods converges weakly to a solution of the variational inequality under some appropriate conditions. The Fejér monotonicity of even subsequence is recovered in these methods and linear rate of convergence is obtained. The numerical implementations of our methods compared with some other inertial projection methods show that our method is more efficient and outperforms some of these inertial projection methods."}],"oa_version":"Submitted Version"},{"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"author":[{"first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","last_name":"Shehu"},{"first_name":"Aviv","full_name":"Gibali, Aviv","last_name":"Gibali"},{"first_name":"Simone","last_name":"Sagratella","full_name":"Sagratella, Simone"}],"article_processing_charge":"No","external_id":{"isi":["000511805200009"]},"title":"Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces","citation":{"chicago":"Shehu, Yekini, Aviv Gibali, and Simone Sagratella. “Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” Journal of Optimization Theory and Applications. Springer Nature, 2020. https://doi.org/10.1007/s10957-019-01616-6.","ista":"Shehu Y, Gibali A, Sagratella S. 2020. Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. 184, 877–894.","mla":"Shehu, Yekini, et al. “Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” Journal of Optimization Theory and Applications, vol. 184, Springer Nature, 2020, pp. 877–894, doi:10.1007/s10957-019-01616-6.","short":"Y. Shehu, A. Gibali, S. Sagratella, Journal of Optimization Theory and Applications 184 (2020) 877–894.","ieee":"Y. Shehu, A. Gibali, and S. Sagratella, “Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces,” Journal of Optimization Theory and Applications, vol. 184. Springer Nature, pp. 877–894, 2020.","ama":"Shehu Y, Gibali A, Sagratella S. Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. 2020;184:877–894. doi:10.1007/s10957-019-01616-6","apa":"Shehu, Y., Gibali, A., & Sagratella, S. (2020). Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. Springer Nature. https://doi.org/10.1007/s10957-019-01616-6"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"We are grateful to the anonymous referees and editor whose insightful comments helped to considerably improve an earlier version of this paper. The research of the first author is supported by an ERC Grant from the Institute of Science and Technology (IST).","page":"877–894","date_published":"2020-03-01T00:00:00Z","doi":"10.1007/s10957-019-01616-6","date_created":"2019-12-09T21:33:44Z","has_accepted_license":"1","isi":1,"year":"2020","day":"01","publication":"Journal of Optimization Theory and Applications","type":"journal_article","article_type":"original","status":"public","_id":"7161","file_date_updated":"2021-03-16T23:30:04Z","department":[{"_id":"VlKo"}],"date_updated":"2023-09-06T11:27:15Z","ddc":["518","510","515"],"scopus_import":"1","month":"03","intvolume":" 184","abstract":[{"text":"In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature.","lang":"eng"}],"oa_version":"Submitted Version","volume":184,"ec_funded":1,"publication_identifier":{"issn":["0022-3239"],"eissn":["1573-2878"]},"publication_status":"published","file":[{"date_updated":"2021-03-16T23:30:04Z","file_size":332641,"creator":"dernst","date_created":"2020-10-12T10:40:27Z","file_name":"2020_JourOptimizationTheoryApplic_Shehu.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"9f6dc6c6bf2b48cb3a2091a9ed5feaf2","file_id":"8647","embargo":"2021-03-15"}],"language":[{"iso":"eng"}]}]