Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2000-002 (May 26, 2000)

Nonlinear Proximal Decomposition Method with Bregman Function for Solving Monotone Variational Inequality Problems
by Masahiro Kyono and Masao Fukushima

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In this paper, we propose a new decomposition method for solving monotone variational inequality problems. The algorithm is an extension of the decomposition method proposed by the authors for solving convex programming problems. To solve subproblems approximately, the algorithm adopts a practical criterion proposed by Solodov and Svaiter for the proximal proximal point algorithm. Under some mild assumptions, global convergence of the proposed algorithm is established.