Optimality Conditions And Continuity Of Generalized Vector Equilibrium Problems

Optimality conditions and stability analysis for vector equilibrium problems are important topics in vector optimization research.Usually,optimality condition can be studied in real linear spaces without topological structure and topological spaces,and stability investigations include upper and lower semi-continuity,Lipschitz continuity,H?lder continuity and so on.In this thesis,scalar characterizations and optimality conditions for vector equilibrium problems in real linear spaces without topological structures are discussed,and the sufficient conditions of continuity for the solutions of parametric generalized weak vector equilibrium problems are established.The scalarization method is a popular and important approach to study vector optimization problems.This thesis also uses this method to solve vector equilibrium problems.In addition,the improvement set provides an effective tool for studying the unity of solutions to vector optimization problems.In this thesis,vector equilibrium problems are discussed under the unified framework based on improvement sets.First,vector equilibrium problems with the ordering relations defined via improvement sets are studied in real linear spaces without assuming any topology.We deal with efficient solutions,weak efficient solutions,Benson and Henig proper efficient solutions.The linear scalarization characterizations of these solutions are established,moreover,optimization conditions via Lagrange multiplier rulers for vector equilibrium problems with constraints are also obtained.Our results generalize the corresponding ones in the literature.Then,this thesis studies the semi-continuity of solution mappings for unified parameter generalized weak vector equilibrium problems with the ordering relations defined using improvement sets.By applying the known sufficient condition that the solution set of the generalized weak vector equilibrium problem can be expressed as the union of solution sets to corresponding linear scalarization problems,and the strict pseudomonotonicity assumption,under the new continuity condition of the objective mapping,continuity conclusions of solutions for the parameter generalized weak vector equilibrium problem under improvement sets are obtained.