An LQP-Based Decomposition Method for Solving a Class of Variational Inequalities

Xiaoming Yuan; Min Li

doi:10.1137/070703557

An LQP-Based Decomposition Method for Solving a Class of Variational Inequalities

Xiaoming Yuan^*, Min Li

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

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Abstract

The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.

Original language	English
Pages (from-to)	1309-1318
Number of pages	10
Journal	SIAM Journal on Optimization
Volume	21
Issue number	4
DOIs	https://doi.org/10.1137/070703557
Publication status	Published - 22 Nov 2011

Scopus Subject Areas

Software
Theoretical Computer Science

User-Defined Keywords

Alternating direction method
Complementarity problem
Logarithmic-quadratic proximal method
System of nonlinear equations
Variational inequality

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10.1137/070703557

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abstract = "The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.",

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note = "Funding information: Corresponding author. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (xmyuan@hkbu.edu.hk). This author was partially supported by Hong Kong General Research Fund grant HKBU 203009 and National Natural Science Foundation of China grant 10701055. School of Economics and Management, Southeast University, Nanjing 210096, China (limin@ seu.edu.cn). This author was supported by National Natural Science Foundation of China grant 11001053 and SRFDP grant 200802861031. Publisher copyright: Copyright {\textcopyright} 2011 Society for Industrial and Applied Mathematics",

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N1 - Funding information: Corresponding author. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (xmyuan@hkbu.edu.hk). This author was partially supported by Hong Kong General Research Fund grant HKBU 203009 and National Natural Science Foundation of China grant 10701055. School of Economics and Management, Southeast University, Nanjing 210096, China (limin@ seu.edu.cn). This author was supported by National Natural Science Foundation of China grant 11001053 and SRFDP grant 200802861031. Publisher copyright: Copyright © 2011 Society for Industrial and Applied Mathematics

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N2 - The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.

AB - The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.

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KW - Complementarity problem

KW - Logarithmic-quadratic proximal method

KW - System of nonlinear equations

KW - Variational inequality

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An LQP-Based Decomposition Method for Solving a Class of Variational Inequalities

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