集值映射互补问题理论及其应用

Point to Set Mapping Complementarity Problem Theory and Application

本文将单位映射变分不等式和互补问题的解的存在性定理推广到集值映射上.讨论了集值映射互补问题的解与Kakutani不动点之间关系,以及集值映射互补问题的解的计算方法.最后给出了它们在不可微规划中的应用.

In this article, the authors extend some existence theorems of the solution of complementarity and some variational inequalities of vector functions to set-valued mapping, and establish the necessary and sufficient condition for the relationship between the solution and Kakutani's fixedpoint. For the calcul-ation of the complementarity problem a simplified fixed-point algorithm and the convergent result of the algorithm are given. And their applications in nondifferentiable optimization are also discussed.