The Optimality Conditions For Directional Benson Minimum Solution

Directional optimization problems are widely used in location management,engineering design and economics.In this thesis,we mainly study the optimality conditions for directional Benson minimum solution,and introduce the concepts of directional Benson minimum solution and Benson directional openness.Then the incompatiblity result between directional Benson minimum solution and Benson directional openness is obtained.On primal spaces,using directional Bouligand derivative,two necessary conditions that a point in the graph of set-valued mappings is a directional Benson minimum solution are obtained.Using approximate sequences and enlargement of cones,a sufficient condition for directional Benson minimum solution is given.On dual spaces,in terms of the separation theorem,directional Bouligand derivative,and the convexity of the set-valued mappings,some characterizations of directional Benson minimum solution are given.