Necessary Conditions For Set-valued Vector Equilibrium Problems And Duality For^ε- Henig Set-value Vector Quasi-equilibrium Problem

In this paper, the optimality research background of the vector equilibrium problems and the duality of the research background of the vector equilibrium problems are introduced in the first chapter. In the second chapter, it gave the relevant basic knowledge.The paper studied necessary conditions of solutions for set-valued vector equilibrium problems in the third chapter. In terms of the concept of coderivative in Clarke sense, the necessary conditions of efficient solution, weakly efficient solution, Henig efficient solution, globally efficient solution to set-valued vector equilibrium problems on Banach spaces are given. By using of the concept of coderivative in Mordukhovich sense, the necessary conditions of solutions for set-valued vector equilibrium problems with constraints without convexity conditions in Asplund spaces are presented.In the fourth chapter, It discussed the duality for ε-Henig set-value vector quasi-equilibrium problem. The ε-Henig vector quasi-equilibrium problem and its dual problem with set-valued mappings are introduced, under the generalized convexity and generalized Slater conditions, the relationships between ε-Henig efficient solutions of ε-Henig vector quasi-equilibrium problem and its dual problem are discussed, the duality theorem of ε-Henig vector quasi-equilibrium problem is given.