Study Of A Class Vector Extremum Problems

This thesis is aimed to study, in Hausdorff topological linear spaces and ordered lin- ear spaces respectively,the optimization problems.Full text is divided into four chapters. In the first chapter, we give some backgroun- ds to the results in the thesis. In the second chapter, we give some preliminary definitions and results. In the following two chapters, we present the main results: in Hausdorff top- ologyical linear spaces and ordered linear spaces respectively, the alternative theorems for ( y , O_Z ;U_+)-generalized subconvexlike(set-valued) maps are given; The optimality c- onditions for vector optimization and set-valued optimization with constraints problems are obtained, and the Lagrange Duality in set-valued optimization is also established. Se- veral equivalent definitions of the ( y , O_Z ;U_+)-generalized subconvexlike set-valued map are given.