The Research Of Several Efficient Solutions On Vector Optimization Problems

The research of the solution of vector optimization problems has become a hot research topic by many scholars in recent decades. On the basis of given vector optimization problems, we analyse the efficient solution’s sufficient and necessary conditions under the speci?c objective function, discuss the stability of solution. Then extend the concept of the existing efficient solution, propose other several kinds of properly efficient solutions,and study their related properties, ?nally probe some properties of solution in complete metric space, the main contents are as follows:1. Contrapose the concept of efficient solution, weakly efficient solution and so on in vector optimization problems, discuss the existence conditions of G-properly efficient solution when the objective function in vector optimization problems has convexity or not.2. Analyse the efficient solution’s stability of two kinds of representative vector optimization problems, consider the relation between efficient solution and G-properly efficient solution.3. Based on the G-properly efficient solution,propose the concept of KT-properly efficient solution, probe its property and discuss its relation with efficient solution and G-properly efficient solution and so on.4. Discuss the property of minimization problem in the complete metric space, analyse the related properties of cardinal number of solution set in the given meaning of distance.