Hilbert空间中多值(S)_+型映象非线性互补问题解的存在性

Existence of the Solution of the Nonlinear Complementarity Problem on Multi-value (S)_+ Type Mapping of Hilbert Space

主要研究一般凸集约束下Hilbert空间多值 (S) +型映象非线性互补问题的解的存在性 .提出了一个例外簇概念 ,给出了互补问题解存在的一个充分条件 ,对于伪单调算子的非线性互补问题 ,它是一个充要条件 .把文献 [1]中互补问题解的存在定理推广到了Hilbert空间的多值 (S) +型映象 .

In this paper, the existence of the solution of th e nonlinear complementarity problem on mult-value (S) + type mapping of Hilb ert space is proved under general constraint convex set. A definition of excep tional families is proposed, and a sufficient condition of the solution of compl ementarity problem is given. To the nonlinear complementarity problem of pseudo- monotone operator, this condition is both sufficient and necessary. This paper e xtends the existence theorem in \to the multi-value (S) + type mapping of Hilbert space.