Application of a Splitting Method to a Class of Non-Monotone Variational Inequalities(<Special Issue>Variational Inequality and Combinatorial Problems)

抄録

The problem of finding a solution to a system of variational inequalities, which can be interpreted as a generalization of a primal-dual variational inequality system and involves non-monotone mappings, is considered. This problem has a great number of applications in Economics, Operations Research, Mathematical Physics and other fields. We suggest this problem to be converted into a variational inequality corresponding to optimality conditions of a non-convex optimization problem. The latter problem is proposed to be solved by a splitting type method.