[{"month":"03","publication_identifier":{"eissn":["1436-4646"],"issn":["0025-5610"]},"language":[{"iso":"eng"}],"doi":"10.1007/s10107-024-02064-5","quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2109.10203"]},"file_date_updated":"2021-09-27T10:54:51Z","article_number":"2109.10203","date_created":"2021-09-27T10:48:23Z","date_updated":"2024-03-19T08:20:31Z","author":[{"last_name":"Dvorak","first_name":"Martin","orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"epub_ahead","publisher":"Springer Nature","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"year":"2024","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).","day":"07","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","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"],"scopus_import":"1","date_published":"2024-03-07T00:00:00Z","article_type":"original","publication":"Mathematical Programming","citation":{"ama":"Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 2024. doi:10.1007/s10107-024-02064-5","ieee":"M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and discrete convexity,” Mathematical Programming. Springer Nature, 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","ista":"Dvorak M, Kolmogorov V. 2024. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming., 2109.10203.","short":"M. Dvorak, V. Kolmogorov, Mathematical Programming (2024).","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.","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."},"abstract":[{"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","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","file":[{"relation":"main_file","file_id":"10046","date_created":"2021-09-27T10:54:51Z","date_updated":"2021-09-27T10:54:51Z","checksum":"e7e83065f7bc18b9c188bf93b5ca5db6","success":1,"file_name":"Generalized-0-Ext.pdf","access_level":"open_access","file_size":603672,"content_type":"application/pdf","creator":"mdvorak"}],"status":"public","title":"Generalized minimum 0-extension problem and discrete convexity","ddc":["004"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10045"},{"month":"07","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959772785"]},"conference":{"name":"ICALP: International Colloquium on Automata, Languages, and Programming","start_date":"2023-07-10","location":"Paderborn, Germany","end_date":"2023-07-14"},"doi":"10.4230/LIPIcs.ICALP.2023.72","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2007.10824"]},"quality_controlled":"1","file_date_updated":"2023-08-21T06:45:16Z","article_number":"72","author":[{"last_name":"Harris","first_name":"David G.","full_name":"Harris, David G."},{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir"}],"date_updated":"2023-08-21T06:49:11Z","date_created":"2023-08-20T22:01:14Z","volume":261,"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.","year":"2023","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"VlKo"}],"day":"01","has_accepted_license":"1","article_processing_charge":"Yes","scopus_import":"1","date_published":"2023-07-01T00:00:00Z","publication":"50th International Colloquium on Automata, Languages, and Programming","citation":{"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.","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.","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","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","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.","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.","short":"D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023."},"abstract":[{"lang":"eng","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."}],"type":"conference","alternative_title":["LIPIcs"],"oa_version":"Published Version","file":[{"relation":"main_file","file_id":"14088","checksum":"6dee0684245bb1c524b9c955db1e933d","success":1,"date_updated":"2023-08-21T06:45:16Z","date_created":"2023-08-21T06:45:16Z","access_level":"open_access","file_name":"2023_LIPIcsICALP_Harris.pdf","content_type":"application/pdf","file_size":917791,"creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14084","status":"public","ddc":["000","510"],"title":"Parameter estimation for Gibbs distributions","intvolume":" 261"},{"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.ITP.2023.15","conference":{"name":"ITP: International Conference on Interactive Theorem Proving","start_date":"2023-07-31","location":"Bialystok, Poland","end_date":"2023-08-04"},"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2302.06420"]},"oa":1,"publication_identifier":{"isbn":["9783959772846"],"eissn":["1868-8969"]},"month":"07","volume":268,"date_updated":"2023-09-25T11:04:29Z","date_created":"2023-06-05T07:29:05Z","related_material":{"link":[{"relation":"software","url":"https://github.com/madvorak/grammars/tree/publish"}]},"author":[{"last_name":"Dvorak","first_name":"Martin","orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin"},{"full_name":"Blanchette, Jasmin","first_name":"Jasmin","last_name":"Blanchette"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"publication_status":"published","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. ","year":"2023","file_date_updated":"2023-08-07T11:55:43Z","article_number":"15","date_published":"2023-07-27T00:00:00Z","citation":{"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.","short":"M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","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.","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","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.","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.","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"},"publication":"14th International Conference on Interactive Theorem Proving","has_accepted_license":"1","article_processing_charge":"No","day":"27","scopus_import":"1","file":[{"creator":"dernst","file_size":715976,"content_type":"application/pdf","access_level":"open_access","file_name":"2023_LIPIcS_Dvorak.pdf","success":1,"checksum":"773a0197f05b67feaa6cb1e17ec3642d","date_created":"2023-08-07T11:55:43Z","date_updated":"2023-08-07T11:55:43Z","file_id":"13982","relation":"main_file"}],"oa_version":"Published Version","intvolume":" 268","status":"public","ddc":["000"],"title":"Closure properties of general grammars - formally verified","_id":"13120","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"alternative_title":["LIPIcs"],"type":"conference"},{"year":"2023","department":[{"_id":"VlKo"}],"publisher":"IEEE","publication_status":"published","author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"volume":2023,"date_updated":"2023-10-31T12:01:24Z","date_created":"2023-10-22T22:01:16Z","publication_identifier":{"isbn":["9798350301298"],"issn":["1063-6919"]},"month":"08","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2010.09567"}],"external_id":{"arxiv":["2010.09567"]},"oa":1,"quality_controlled":"1","doi":"10.1109/CVPR52729.2023.01153","conference":{"name":"CVPR: Conference on Computer Vision and Pattern Recognition","end_date":"2023-06-24","start_date":"2023-06-17","location":"Vancouver, Canada"},"language":[{"iso":"eng"}],"type":"conference","abstract":[{"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.","lang":"eng"}],"_id":"14448","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 2023","title":"Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions","status":"public","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"22","citation":{"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.","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","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.","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.","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."},"publication":"Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition","page":"11980-11989","date_published":"2023-08-22T00:00:00Z"},{"publication_identifier":{"issn":["1088-467X"],"eissn":["1571-4128"]},"month":"01","quality_controlled":"1","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1404.5475","open_access":"1"}],"oa":1,"external_id":{"isi":["000749997700015"],"arxiv":["1404.5475"]},"language":[{"iso":"eng"}],"doi":"10.3233/IDA-205623","publisher":"IOS Press","department":[{"_id":"VlKo"}],"publication_status":"published","year":"2022","volume":26,"date_created":"2022-02-06T23:01:32Z","date_updated":"2023-08-02T14:09:41Z","author":[{"full_name":"Takhanov, Rustem","id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87","last_name":"Takhanov","first_name":"Rustem"},{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"}],"scopus_import":"1","article_processing_charge":"No","day":"14","page":"257-272","article_type":"original","citation":{"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.","short":"R. Takhanov, V. Kolmogorov, Intelligent Data Analysis 26 (2022) 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.","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","ista":"Takhanov R, Kolmogorov V. 2022. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 26(1), 257–272.","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.","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"},"publication":"Intelligent Data Analysis","date_published":"2022-01-14T00:00:00Z","type":"journal_article","issue":"1","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"}],"intvolume":" 26","title":"Combining pattern-based CRFs and weighted context-free grammars","status":"public","_id":"10737","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint"},{"scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"01","page":"192-216","article_type":"original","citation":{"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.","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.","short":"Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216.","ista":"Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216.","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.","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"},"publication":"Applicable Analysis","date_published":"2022-01-01T00:00:00Z","type":"journal_article","issue":"1","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."}],"intvolume":" 101","title":"Weak convergence for variational inequalities with inertial-type method","status":"public","ddc":["510","515","518"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7577","file":[{"file_size":4282586,"content_type":"application/pdf","creator":"dernst","file_name":"2020_ApplicAnalysis_Shehu.pdf","access_level":"open_access","date_updated":"2021-03-16T23:30:06Z","date_created":"2020-10-12T10:42:54Z","checksum":"869efe8cb09505dfa6012f67d20db63d","relation":"main_file","file_id":"8648","embargo":"2021-03-15"}],"oa_version":"Submitted Version","publication_identifier":{"issn":["0003-6811"],"eissn":["1563-504X"]},"month":"01","project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"external_id":{"arxiv":["2101.08057"],"isi":["000518364100001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1080/00036811.2020.1736287","ec_funded":1,"file_date_updated":"2021-03-16T23:30:06Z","publisher":"Taylor & Francis","department":[{"_id":"VlKo"}],"publication_status":"published","year":"2022","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).","volume":101,"date_created":"2020-03-09T07:06:52Z","date_updated":"2024-03-05T14:01:52Z","author":[{"full_name":"Shehu, Yekini","first_name":"Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139"},{"first_name":"Olaniyi S.","last_name":"Iyiola","full_name":"Iyiola, Olaniyi S."}]},{"ec_funded":1,"file_date_updated":"2021-10-06T13:51:54Z","article_number":"31","volume":207,"date_created":"2021-10-03T22:01:22Z","date_updated":"2022-03-18T10:08:25Z","author":[{"last_name":"Harris","first_name":"David G.","full_name":"Harris, David G."},{"full_name":"Iliopoulos, Fotis","first_name":"Fotis","last_name":"Iliopoulos"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","department":[{"_id":"VlKo"}],"publication_status":"published","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.","year":"2021","publication_identifier":{"isbn":["978-3-9597-7207-5"],"issn":["1868-8969"]},"month":"09","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.APPROX/RANDOM.2021.31","conference":{"end_date":"2021-08-18","start_date":"2021-08-16","location":"Virtual","name":"APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation"},"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2008.05569"]},"oa":1,"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."}],"alternative_title":["LIPIcs"],"type":"conference","file":[{"creator":"cchlebak","content_type":"application/pdf","file_size":804472,"file_name":"2021_LIPIcs_Harris.pdf","access_level":"open_access","date_created":"2021-10-06T13:51:54Z","date_updated":"2021-10-06T13:51:54Z","success":1,"checksum":"9d2544d53aa5b01565c6891d97a4d765","file_id":"10098","relation":"main_file"}],"oa_version":"Published Version","intvolume":" 207","status":"public","title":"A new notion of commutativity for the algorithmic Lovász Local Lemma","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10072","has_accepted_license":"1","article_processing_charge":"Yes","day":"15","scopus_import":"1","date_published":"2021-09-15T00:00:00Z","citation":{"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","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.","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.","short":"D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","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.","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."},"publication":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques"},{"ec_funded":1,"abstract":[{"lang":"eng","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."}],"type":"conference","oa_version":"Preprint","date_updated":"2021-12-17T09:06:46Z","date_created":"2021-12-16T12:41:20Z","author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pock, Thomas","last_name":"Pock","first_name":"Thomas"}],"department":[{"_id":"VlKo"}],"title":"One-sided Frank-Wolfe algorithms for saddle problems","publication_status":"published","status":"public","_id":"10552","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.","year":"2021","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_processing_charge":"No","day":"01","month":"07","language":[{"iso":"eng"}],"date_published":"2021-07-01T00:00:00Z","conference":{"name":"ICML: International Conference on Machine Learning","end_date":"2021-07-24","location":"Virtual","start_date":"2021-07-18"},"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.12617"}],"oa":1,"external_id":{"arxiv":["2101.12617"]},"citation":{"ieee":"V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,” in 38th International Conference on Machine Learning, Virtual, 2021.","apa":"Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for saddle problems. In 38th International Conference on Machine Learning. Virtual.","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.","ama":"Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems. In: 38th International Conference on Machine Learning. ; 2021.","chicago":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” In 38th International Conference on Machine Learning, 2021.","short":"V. Kolmogorov, T. Pock, 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."},"publication":"38th International Conference on Machine Learning"},{"publication_status":"accepted","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"year":"2021","date_created":"2021-06-22T15:57:11Z","date_updated":"2021-08-12T10:57:39Z","author":[{"last_name":"Dvorak","first_name":"Martin","orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin"},{"full_name":"Nicholson, Sara","last_name":"Nicholson","first_name":"Sara"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","file_date_updated":"2021-08-12T10:57:21Z","quality_controlled":"1","oa":1,"tmp":{"short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"external_id":{"arxiv":["2106.11247"]},"language":[{"iso":"eng"}],"conference":{"name":"CCCG: Canadian Conference on Computational Geometry","end_date":"2021-08-12","start_date":"2021-08-10","location":"Halifax, NS, Canada"},"month":"06","status":"public","title":"Massively winning configurations in the convex grabbing game on the plane","ddc":["516"],"_id":"9592","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","file_name":"Convex-Grabbing-Game_CCCG_proc_version.pdf","creator":"mdvorak","content_type":"application/pdf","file_size":381306,"file_id":"9616","relation":"main_file","success":1,"checksum":"45accb1de9b7e0e4bb2fbfe5fd3e6239","date_updated":"2021-06-28T20:23:13Z","date_created":"2021-06-28T20:23:13Z"},{"relation":"main_file","file_id":"9902","checksum":"9199cf18c65658553487458cc24d0ab2","success":1,"date_updated":"2021-08-12T10:57:21Z","date_created":"2021-08-12T10:57:21Z","access_level":"open_access","file_name":"Convex-Grabbing-Game_FULL-VERSION.pdf","content_type":"application/pdf","file_size":403645,"creator":"kschuh"}],"oa_version":"Submitted Version","type":"conference","abstract":[{"lang":"eng","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."}],"publication":"Proceedings of the 33rd Canadian Conference on Computational Geometry","citation":{"short":"M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference on Computational Geometry, n.d.","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.","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.","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.","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.","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."},"date_published":"2021-06-29T00:00:00Z","keyword":["convex grabbing game","graph grabbing game","combinatorial game","convex geometry"],"day":"29","article_processing_charge":"No","has_accepted_license":"1"},{"isi":1,"quality_controlled":"1","project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"}],"external_id":{"isi":["000650507600001"]},"language":[{"iso":"eng"}],"doi":"10.1080/10556788.2021.1924715","month":"05","publication_identifier":{"eissn":["1029-4937"],"issn":["1055-6788"]},"publication_status":"published","publisher":"Taylor and Francis","department":[{"_id":"VlKo"}],"year":"2021","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).","date_created":"2021-06-06T22:01:30Z","date_updated":"2023-08-08T13:57:43Z","author":[{"full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola","first_name":"Olaniyi S."},{"first_name":"Cyril D.","last_name":"Enyi","full_name":"Enyi, Cyril D."},{"full_name":"Shehu, Yekini","last_name":"Shehu","first_name":"Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"}],"ec_funded":1,"article_type":"original","publication":"Optimization Methods and Software","citation":{"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","ista":"Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software.","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.","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.","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."},"date_published":"2021-05-12T00:00:00Z","scopus_import":"1","day":"12","article_processing_charge":"No","title":"Reflected three-operator splitting method for monotone inclusion problem","status":"public","_id":"9469","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"None","type":"journal_article","abstract":[{"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.","lang":"eng"}]}]