| Mayor: Operation and Control Theory Author: Cheng-jia Gao Advisor: Prof. Nan-jing HuangAbstract: This paper includes two chapters.In the first part, we concerns optimization problems with quasi-variational inequality constraints. Using the generalized differential caculus for multi-mappings or nonsmooth mappings in finite demensional spaces which is dued to S.B. Morduhovich, we derive necessary optimal conditions for this class of optimal problems. In the first section, we show the background of the problems that we study, which comes from applied science, and in the second section, we introduce the generalized differential caculus for multi-mappings or nonsmooth mappings in finite demensional spaces, which is dued to S.B. Morduhovich, and their properties. Our main results are in the last two sections. Section 3 is devoted to the stablities for the perturbed generalized equations. With some constraint qualifications, the pseudo-Lipschitz continuities for solution mappings of generalized equations at the solutions is obtained, which implicits the pseudo-upper-Lipschitz continuity at the same points. In the last, we derive necessary optimal conditions for optimal problems with quasi-variational inequalities.In the second chapter, we study the existence of generalized complementarity problem by introducing exceptional family, which is a topological method in nature. As a new way to study complementarity problems, we mainly prove the existed results by using the concept of exceptional family as well as some new results, in the first section of this chapter,we draw the conclusion that generalized complementarity problems either are solvable or have an exceptional family of /, and obtain the results that generalized complementarity problems have solutions. And later, we discuss the feasibility of generalized complementarity problems. |
