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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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 437
Main Authors Wang, Feiran, Yuan, Yuan, Wang, Xiaoquan, Shao, Hu, Shen, Liang
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2024
Subjects
Linear complementarity problem
Lineared subproblem
Sequential ADMM
Sparse solution
Linear complementarity problem
Sparse solution
Sequential ADMM
Lineared subproblem
Online AccessGet full text
ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2023.115470

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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115470