Properties And Stability Of Several Kind Of Solutions For Set-valued Optimization Problems

In this thesis,we make further research about the properties and stability of approximate Henig efficient points,E-Henig efficient solutions for the set-valued optimization problems,when the objective function and feasible region of the set-valued optimization problems are perturbed.At the same time,under the condition that the objective function and feasible region of the vector optimization problems are perturbed,we obtain the stability results of Benson efficient solutions for the vector optimization problems.This thesis is divided into six chapters.It is organized as follows:In Chapter 1,we introduce the current researches of several kinds of solutions for set-valued optimization problems.We also give the main work and significance of this thesis.In Chapter 2,we give the model of the set-valued optimization problems and the vector optimization problems.Meanwhile,we introduce the definitions and properties of approximate Henig efficient solutions,E-Henig efficient solutions,and Benson efficient solutions.Some concepts of convergence and convexity are also introduced.In Chapter 3,firstly,we give the concept of(38)_C convergence of set-valued function sequence,by comparing the relationship between the(38)_C convergence and the Painlevé-Kuratowski convergence,we found the Painlevé-Kuratowski convergence is weaker than(38)_C convergence.Secondly,we apply the Painlevé-Kuratowski converg-ence to establish the stability of approximate Henig efficient points for the set-valued optimization problems,and we obtain the stability of approximate Henig effective points for the set-valued optimization problems when the data of the perturbed problems converges to the data of the original problems in the sense of Painlevé-Kuratowski.In Chapter 4,at the beginning,based on the concept of improved set,we introduce E-Henig efficient solutions for set-valued optimization problems,and it unifies the approximate Henig efficient solutions and the Henig efficient solutions for the set-valued optimization problem.Furthermore under the condition that the objective function and constraint conditions are perturbed,we use Painlevé-Kuratowski converg-ence to obtain the stability of the E-Henig effective point sets and E-Henig effective solution sets for strictly proper quasi C-convex set-valued optimization problem.In Chapter 5,at first,we establish the equivalent relationship between Benson efficient solutions for vector optimization problems and the solution of a class of scalar optimization problems by using nonlinear scaling technique.Besides,with the means of the equivalence result,we obtain the stability results of Benson efficient point sets and the solution sets in the vector optimization problems when the objective function and the constraint conditions are perturbed.In Chapter 6,the results of this thesis are briefly summarized.And we put forward some remaining problems and prospects.