--- _id: '6725' abstract: - lang: eng text: "A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language. \r\nRecent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds." alternative_title: - LIPIcs author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Kolmogorov V. Testing the complexity of a valued CSP language. In: 46th International Colloquium on Automata, Languages and Programming. Vol 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:77:1-77:12. doi:10.4230/LIPICS.ICALP.2019.77' apa: 'Kolmogorov, V. (2019). Testing the complexity of a valued CSP language. In 46th International Colloquium on Automata, Languages and Programming (Vol. 132, p. 77:1-77:12). Patras, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ICALP.2019.77' chicago: Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” In 46th International Colloquium on Automata, Languages and Programming, 132:77:1-77:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.ICALP.2019.77. ieee: V. Kolmogorov, “Testing the complexity of a valued CSP language,” in 46th International Colloquium on Automata, Languages and Programming, Patras, Greece, 2019, vol. 132, p. 77:1-77:12. ista: 'Kolmogorov V. 2019. Testing the complexity of a valued CSP language. 46th International Colloquium on Automata, Languages and Programming. ICALP 2019: International Colloquim on Automata, Languages and Programming, LIPIcs, vol. 132, 77:1-77:12.' mla: Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” 46th International Colloquium on Automata, Languages and Programming, vol. 132, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12, doi:10.4230/LIPICS.ICALP.2019.77. short: V. Kolmogorov, in:, 46th International Colloquium on Automata, Languages and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12. conference: end_date: 2019-07-12 location: Patras, Greece name: 'ICALP 2019: International Colloquim on Automata, Languages and Programming' start_date: 2019-07-08 date_created: 2019-07-29T12:23:29Z date_published: 2019-07-01T00:00:00Z date_updated: 2021-01-12T08:08:40Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.4230/LIPICS.ICALP.2019.77 ec_funded: 1 external_id: arxiv: - '1803.02289' file: - access_level: open_access checksum: f5ebee8eec6ae09e30365578ee63a492 content_type: application/pdf creator: dernst date_created: 2019-07-31T07:01:45Z date_updated: 2020-07-14T12:47:38Z file_id: '6738' file_name: 2019_LIPICS_Kolmogorov.pdf file_size: 575475 relation: main_file file_date_updated: 2020-07-14T12:47:38Z has_accepted_license: '1' intvolume: ' 132' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 77:1-77:12 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: 46th International Colloquium on Automata, Languages and Programming publication_identifier: isbn: - 978-3-95977-109-2 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Testing the complexity of a valued CSP language tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 132 year: '2019' ... --- _id: '6596' abstract: - lang: eng text: It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper. article_number: '138' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Shehu Y. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 2019;74(4). doi:10.1007/s00025-019-1061-4 apa: Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. Springer. https://doi.org/10.1007/s00025-019-1061-4 chicago: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics. Springer, 2019. https://doi.org/10.1007/s00025-019-1061-4. ieee: Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces,” Results in Mathematics, vol. 74, no. 4. Springer, 2019. ista: Shehu Y. 2019. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138. mla: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics, vol. 74, no. 4, 138, Springer, 2019, doi:10.1007/s00025-019-1061-4. short: Y. Shehu, Results in Mathematics 74 (2019). date_created: 2019-06-29T10:11:30Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-08-28T12:26:22Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.1007/s00025-019-1061-4 ec_funded: 1 external_id: arxiv: - '2101.09068' isi: - '000473237500002' file: - access_level: open_access checksum: c6d18cb1e16fc0c36a0e0f30b4ebbc2d content_type: application/pdf creator: kschuh date_created: 2019-07-03T15:20:40Z date_updated: 2020-07-14T12:47:34Z file_id: '6605' file_name: Springer_2019_Shehu.pdf file_size: 466942 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 74' isi: 1 issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Results in Mathematics publication_identifier: eissn: - 1420-9012 issn: - 1422-6383 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 74 year: '2019' ... --- _id: '7000' abstract: - lang: eng text: The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps. article_number: '161' article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Xiao-Huan full_name: Li, Xiao-Huan last_name: Li - first_name: Qiao-Li full_name: Dong, Qiao-Li last_name: Dong citation: ama: Shehu Y, Iyiola OS, Li X-H, Dong Q-L. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 2019;38(4). doi:10.1007/s40314-019-0955-9 apa: Shehu, Y., Iyiola, O. S., Li, X.-H., & Dong, Q.-L. (2019). Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. Springer Nature. https://doi.org/10.1007/s40314-019-0955-9 chicago: Shehu, Yekini, Olaniyi S. Iyiola, Xiao-Huan Li, and Qiao-Li Dong. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics. Springer Nature, 2019. https://doi.org/10.1007/s40314-019-0955-9. ieee: Y. Shehu, O. S. Iyiola, X.-H. Li, and Q.-L. Dong, “Convergence analysis of projection method for variational inequalities,” Computational and Applied Mathematics, vol. 38, no. 4. Springer Nature, 2019. ista: Shehu Y, Iyiola OS, Li X-H, Dong Q-L. 2019. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 38(4), 161. mla: Shehu, Yekini, et al. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics, vol. 38, no. 4, 161, Springer Nature, 2019, doi:10.1007/s40314-019-0955-9. short: Y. Shehu, O.S. Iyiola, X.-H. Li, Q.-L. Dong, Computational and Applied Mathematics 38 (2019). date_created: 2019-11-12T12:41:44Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-08-30T07:20:32Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1007/s40314-019-0955-9 ec_funded: 1 external_id: arxiv: - '2101.09081' isi: - '000488973100005' has_accepted_license: '1' intvolume: ' 38' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s40314-019-0955-9 month: '12' oa: 1 oa_version: Published Version project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Computational and Applied Mathematics publication_identifier: eissn: - 1807-0302 issn: - 2238-3603 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Convergence analysis of projection method for variational inequalities type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 38 year: '2019' ... --- _id: '7412' abstract: - lang: eng text: We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These algorithms search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a random nearby state that addresses the violation, while (we hope) not introducing many new violations. An important class of focused local search algorithms with provable performance guarantees has recently arisen from algorithmizations of the Lovász local lemma (LLL), a nonconstructive tool for proving the existence of satisfying states by introducing a background measure on the state space. While powerful, the state transitions of algorithms in this class must be, in a precise sense, perfectly compatible with the background measure. In many applications this is a very restrictive requirement, and one needs to step outside the class. Here we introduce the notion of measure distortion and develop a framework for analyzing arbitrary focused stochastic local search algorithms, recovering LLL algorithmizations as the special case of no distortion. Our framework takes as input an arbitrary algorithm of such type and an arbitrary probability measure and shows how to use the measure as a yardstick of algorithmic progress, even for algorithms designed independently of the measure. article_processing_charge: No article_type: original author: - first_name: Dimitris full_name: Achlioptas, Dimitris last_name: Achlioptas - first_name: Fotis full_name: Iliopoulos, Fotis last_name: Iliopoulos - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Achlioptas D, Iliopoulos F, Kolmogorov V. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 2019;48(5):1583-1602. doi:10.1137/16m109332x apa: Achlioptas, D., Iliopoulos, F., & Kolmogorov, V. (2019). A local lemma for focused stochastical algorithms. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/16m109332x chicago: Achlioptas, Dimitris, Fotis Iliopoulos, and Vladimir Kolmogorov. “A Local Lemma for Focused Stochastical Algorithms.” SIAM Journal on Computing. SIAM, 2019. https://doi.org/10.1137/16m109332x. ieee: D. Achlioptas, F. Iliopoulos, and V. Kolmogorov, “A local lemma for focused stochastical algorithms,” SIAM Journal on Computing, vol. 48, no. 5. SIAM, pp. 1583–1602, 2019. ista: Achlioptas D, Iliopoulos F, Kolmogorov V. 2019. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 48(5), 1583–1602. mla: Achlioptas, Dimitris, et al. “A Local Lemma for Focused Stochastical Algorithms.” SIAM Journal on Computing, vol. 48, no. 5, SIAM, 2019, pp. 1583–602, doi:10.1137/16m109332x. short: D. Achlioptas, F. Iliopoulos, V. Kolmogorov, SIAM Journal on Computing 48 (2019) 1583–1602. date_created: 2020-01-30T09:27:32Z date_published: 2019-10-31T00:00:00Z date_updated: 2023-09-06T15:25:29Z day: '31' department: - _id: VlKo doi: 10.1137/16m109332x ec_funded: 1 external_id: arxiv: - '1809.01537' isi: - '000493900200005' intvolume: ' 48' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1809.01537 month: '10' oa: 1 oa_version: Preprint page: 1583-1602 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM quality_controlled: '1' scopus_import: '1' status: public title: A local lemma for focused stochastical algorithms type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 48 year: '2019' ... --- _id: '7468' abstract: - lang: eng text: We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane block-coordinate Frank-Wolfe method that takes advantage of the specific structure of the Lagrangean decomposition. We show empirically that our method outperforms state-of-the-art Lagrangean decomposition based algorithms on some challenging Markov Random Field, multi-label discrete tomography and graph matching problems. article_number: 11138-11147 article_processing_charge: No author: - first_name: Paul full_name: Swoboda, Paul id: 446560C6-F248-11E8-B48F-1D18A9856A87 last_name: Swoboda - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Swoboda P, Kolmogorov V. Map inference via block-coordinate Frank-Wolfe algorithm. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol 2019-June. IEEE; 2019. doi:10.1109/CVPR.2019.01140' apa: 'Swoboda, P., & Kolmogorov, V. (2019). Map inference via block-coordinate Frank-Wolfe algorithm. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 2019–June). Long Beach, CA, United States: IEEE. https://doi.org/10.1109/CVPR.2019.01140' chicago: Swoboda, Paul, and Vladimir Kolmogorov. “Map Inference via Block-Coordinate Frank-Wolfe Algorithm.” In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2019–June. IEEE, 2019. https://doi.org/10.1109/CVPR.2019.01140. ieee: P. Swoboda and V. Kolmogorov, “Map inference via block-coordinate Frank-Wolfe algorithm,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Long Beach, CA, United States, 2019, vol. 2019–June. ista: 'Swoboda P, Kolmogorov V. 2019. Map inference via block-coordinate Frank-Wolfe algorithm. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition vol. 2019–June, 11138–11147.' mla: Swoboda, Paul, and Vladimir Kolmogorov. “Map Inference via Block-Coordinate Frank-Wolfe Algorithm.” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2019–June, 11138–11147, IEEE, 2019, doi:10.1109/CVPR.2019.01140. short: P. Swoboda, V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2019. conference: end_date: 2019-06-20 location: Long Beach, CA, United States name: 'CVPR: Conference on Computer Vision and Pattern Recognition' start_date: 2019-06-15 date_created: 2020-02-09T23:00:52Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-07T14:54:24Z day: '01' department: - _id: VlKo doi: 10.1109/CVPR.2019.01140 ec_funded: 1 external_id: arxiv: - '1806.05049' isi: - '000542649304076' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1806.05049 month: '06' oa: 1 oa_version: Preprint project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition publication_identifier: isbn: - '9781728132938' issn: - '10636919' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: Map inference via block-coordinate Frank-Wolfe algorithm type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 2019-June year: '2019' ...