An Inexact Alternating Direction Method for Structured Variational Inequalities

Zhongming Chen (), Li Wan () and Qingzhi Yang ()
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Zhongming Chen: Nankai University
Li Wan: Nankai University
Qingzhi Yang: Nankai University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 2, No 5, 439-459

Abstract: Abstract Recently, the alternating direction method of multipliers has attracted great attention. For a class of variational inequalities (VIs), this method is efficient, when the subproblems can be solved exactly. However, the subproblems could be too difficult or impossible to be solved exactly in many practical applications. In this paper, we propose an inexact method for structured VIs based on the projection and contraction method. Instead of solving the subproblems exactly, we use the simple projection to get a predictor and correct it to approximate the subproblems’ real solutions. The convergence of the proposed method is proved under mild assumptions and its efficiency is also verified by some numerical experiments.

Keywords: Variational inequalities; Alternating direction methods; Projection and contraction methods; 65K05; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-014-0522-x

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