A sequential ADMM algorithm to find sparse LCP solutions using a l2−l1 regularization technique with application in bimatrix game
The linear complementary problem (LCP) is a unified formulation for linear and quadratic programming problems. Therefore, it has many applications in practical problems like bimatrix game. We prove that it makes sense to look for sparse LCP solutions. A l2−l1 regularization technique transforms the...
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| Published in | Journal of computational and applied mathematics Vol. 437 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.02.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2023.115470 |
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| Abstract | The linear complementary problem (LCP) is a unified formulation for linear and quadratic programming problems. Therefore, it has many applications in practical problems like bimatrix game. We prove that it makes sense to look for sparse LCP solutions. A l2−l1 regularization technique transforms the original sparse optimization problem into an unconstrained one. Thereafter, a linearized ADMM (for alternating direction method of multipliers) is designed to solve the regularization model. Then, using a penalty function approach, we propose an efficient sequential linearized ADMM to find the sparse LCP solutions. Finally, numerical experiments prove that the sparse solution of LCPs can be solved efficiently, and is competitive with other state-of-the-art algorithms. A practical application in bimatrix game is also reported. |
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| AbstractList | The linear complementary problem (LCP) is a unified formulation for linear and quadratic programming problems. Therefore, it has many applications in practical problems like bimatrix game. We prove that it makes sense to look for sparse LCP solutions. A l2−l1 regularization technique transforms the original sparse optimization problem into an unconstrained one. Thereafter, a linearized ADMM (for alternating direction method of multipliers) is designed to solve the regularization model. Then, using a penalty function approach, we propose an efficient sequential linearized ADMM to find the sparse LCP solutions. Finally, numerical experiments prove that the sparse solution of LCPs can be solved efficiently, and is competitive with other state-of-the-art algorithms. A practical application in bimatrix game is also reported. |
| ArticleNumber | 115470 |
| Author | Wang, Feiran Shen, Liang Shao, Hu Yuan, Yuan Wang, Xiaoquan |
| Author_xml | – sequence: 1 givenname: Feiran surname: Wang fullname: Wang, Feiran email: wfrlyy@126.com organization: College of Systems Engineering, National University of Defense Technology, Changsha 410073, China – sequence: 2 givenname: Yuan surname: Yuan fullname: Yuan, Yuan email: yyuan_1023@126.com organization: School of Science, Guilin University of Aerospace Technology, Guilin, Guangxi 541004, China – sequence: 3 givenname: Xiaoquan surname: Wang fullname: Wang, Xiaoquan email: wxq4869@163.com organization: School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China – sequence: 4 givenname: Hu orcidid: 0000-0001-7816-0707 surname: Shao fullname: Shao, Hu email: shaohu@cumt.edu.cn organization: School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China – sequence: 5 givenname: Liang orcidid: 0000-0003-4290-5097 surname: Shen fullname: Shen, Liang email: liang_shen@cumt.edu.cn organization: School of Management, Xuzhou Medical University, Xuzhou, Jiangsu 221116, China |
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| Copyright | 2023 Elsevier B.V. |
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| DOI | 10.1016/j.cam.2023.115470 |
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| References | Kingsbury (b8) 2001; 10 Cottle, Pang, Stone (b1) 2009 Shi, Ling, Yuan, Wu, Yin (b28) 2014; 62 Daubechies, Defrise, De Mol (b6) 2004; 57 Geiger, Kanzow (b26) 1996; 5 Fischer (b24) 1995; 86 Jian, Zhang, Liu (b16) 2023; 43 Pardalos, Ketabchi, Moosaei (b4) 2014; 63 Donoho (b7) 1995; 41 Shang, Zhang, Xiu (b5) 2014; 163 Fornasier, Rauhut (b9) 2015 Chen, Li, Liu, Ye (b18) 2019; 173 Illés, Nagy, Terlaky (b30) 2010; 47 Bauschke, Combettes (b23) 2011 Eaves (b2) 1971; 17 Chen, Xiang (b10) 2016; 159 Clarke (b22) 1990 Kojima, Mizuno, Yoshise (b29) 1991; 50 Chen, He, Ye, Yuan (b27) 2016; 155 Shang, Nie (b11) 2014; 2014 Li, Wu (b17) 2021; 38 Wang, Yin, Zeng (b13) 2019; 78 Boyd, Parikh, Chu, Peleato, Eckstein (b14) 2011; 3 Yang, Zhang (b12) 2011; 33 Jiang, Zhang, Lv, Du, Yan (b19) 2020; 76 Facchinei, Pang (b3) 2003 Beck (b21) 2017 Wang, Yan, Jin, Li (b20) 2019; 51 Sun, Li, Xu (b15) 2016; 29 Chen (b25) 2006; 36 |
| References_xml | – volume: 57 start-page: 1413 year: 2004 end-page: 1457 ident: b6 article-title: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint publication-title: Comm. Pure Appl. Math. – volume: 43 start-page: 1 year: 2023 end-page: 24 ident: b16 article-title: A superlinearly convergent splitting feasible sequential quadratic optimization method for two-block large-scale smooth optimization publication-title: Acta Math. Sci. – volume: 62 start-page: 1750 year: 2014 end-page: 1761 ident: b28 article-title: On the linear convergence of the ADMM in decentralized consensus optimization publication-title: IEEE Trans. Signal Process. – year: 2015 ident: b9 publication-title: Compressive Sensing – volume: 63 start-page: 359 year: 2014 end-page: 369 ident: b4 article-title: Minimum norm solution to the positive semidefinite linear complementarity problem publication-title: Optimization – volume: 173 start-page: 37 year: 2019 end-page: 77 ident: b18 article-title: Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights publication-title: Math. Program. – year: 2011 ident: b23 article-title: Convex analysis and monotone operator theory in Hilbert spaces publication-title: CMS Books in Mathematics – volume: 5 start-page: 155 year: 1996 end-page: 173 ident: b26 article-title: On the resolution of monotone complementarity problems publication-title: Comput. Optim. Appl. – volume: 2014 start-page: 1 year: 2014 end-page: 10 ident: b11 article-title: A shrinkage-thresholding projection method for sparsest solutions of LCPs publication-title: J. Inequal. Appl. – year: 2017 ident: b21 article-title: First-Order Methods in Optimization, SIAM – volume: 17 start-page: 612 year: 1971 end-page: 634 ident: b2 article-title: The linear complementarity problem publication-title: Manage. Sci. – year: 2003 ident: b3 article-title: Finite-Dimensional Variational Inequalities and Complementarity Problems – volume: 78 start-page: 29 year: 2019 end-page: 63 ident: b13 article-title: Global convergence of ADMM in nonconvex nonsmooth optimization publication-title: J. Sci. Comput. – volume: 163 start-page: 795 year: 2014 end-page: 814 ident: b5 article-title: Minimal zero norm solutions of linear complementarity problems publication-title: J. Optim. Theory Appl. – volume: 10 start-page: 234 year: 2001 end-page: 253 ident: b8 article-title: Complex wavelets for shift invariant analysis and filtering of signals publication-title: Appl. Comput. Harmon. Anal. – volume: 3 start-page: 1 year: 2011 end-page: 122 ident: b14 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. – year: 1990 ident: b22 article-title: Optimization and Nonsmooth Analysis, SIAM – volume: 38 year: 2021 ident: b17 article-title: On the convergence rate of inexact majorized sGS ADMM with indefinite proximal terms for convex composite programming publication-title: Asia. Pac. J. Oper. Res. – volume: 47 start-page: 329 year: 2010 end-page: 342 ident: b30 article-title: A polynomial path-following interior point algorithm for general linear complementarity problems publication-title: J. Global Optim. – volume: 29 year: 2016 ident: b15 article-title: Deep ADMM-net for compressive sensing MRI publication-title: Adv. Neural Inf. Process. Syst. – volume: 51 start-page: 4540 year: 2019 end-page: 4552 ident: b20 article-title: Distributed and parallel ADMM for structured nonconvex optimization problem publication-title: IEEE Trans. Cybern. – volume: 36 start-page: 565 year: 2006 end-page: 580 ident: b25 article-title: The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem publication-title: J. Global Optim. – volume: 155 start-page: 57 year: 2016 end-page: 79 ident: b27 article-title: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent publication-title: Math. Program. – volume: 76 start-page: 793 year: 2020 end-page: 818 ident: b19 article-title: An ADMM-based location–allocation algorithm for nonconvex constrained multi-source Weber problem under gauge publication-title: J. Global Optim. – volume: 159 start-page: 539 year: 2016 end-page: 556 ident: b10 article-title: Sparse solutions of linear complementarity problems publication-title: Math. Program. – volume: 86 start-page: 585 year: 1995 end-page: 608 ident: b24 article-title: A Newton-type method for positive-semidefinite linear complementarity problems publication-title: J. Optim. Theory Appl. – year: 2009 ident: b1 article-title: The Linear Complementarity Problem, SIAM – volume: 50 start-page: 331 year: 1991 end-page: 342 ident: b29 article-title: An iteration potential reduction algorithm for linear complementarity problems publication-title: Math. program. – volume: 33 start-page: 250 year: 2011 end-page: 278 ident: b12 article-title: Alternating direction algorithms for publication-title: SIAM J. Sci. Comput. – volume: 41 start-page: 613 year: 1995 end-page: 627 ident: b7 article-title: De-noising by soft-thresholding publication-title: IEEE Trans. Inform. Theory |
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| SubjectTerms | Linear complementarity problem Lineared subproblem Sequential ADMM Sparse solution |
| Title | A sequential ADMM algorithm to find sparse LCP solutions using a l2−l1 regularization technique with application in bimatrix game |
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