An improved proximal-based decomposition method for structured monotone variational inequalities

Abstract

The proximal-based decomposition method was originally proposed by Chen and Teboulle (Math. Programming, 1994, 64: 81-101 for solving convex minimization problems. This paper extends it to solving monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem's data as the original method. © 2007 Editorial Committee of Appl. Math. Mech.