A New Decomposition Method for Variational Inequalities with Linear Constraints

Min Zhang, Deren Han (), Gang Qian and Xihong Yan
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Min Zhang: Nanjing Normal University
Deren Han: Nanjing Normal University
Gang Qian: Nanjing Normal University
Xihong Yan: Taiyuan Normal University

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 7, 675-695

Abstract: Abstract We propose a new decomposition method for solving a class of monotone variational inequalities with linear constraints. The proposed method needs only to solve a well-conditioned system of nonlinear equations, which is much easier than a variational inequality, the subproblem in the classic alternating direction methods. To make the method more flexible and practical, we solve the sub-problems approximately. We adopt a self-adaptive rule to adjust the parameter, which can improve the numerical performance of the algorithm. Under mild conditions, the underlying mapping be monotone and the solution set of the problem be nonempty, we prove the global convergence of the proposed algorithm. Finally, we report some preliminary computational results, which demonstrate the promising performance of the new algorithm.

Keywords: Variational inequalities; Decomposition methods; Approximate solution; Self-adaptive; Global convergence (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9931-2

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