The Optimality Conditions For Solutions Of Nonconvex Set-valued Optimization Problems

Set-valued optimization problem includes vector optimization,multi-objective opti-mization problem as special cases,which is a kind of mathematical model close to real life It is widely used in economic equilibrium,stochastic programming,fuzzy programming.optimal control and the other areas.This thesis studies optimality conditions for solu-tions of set-valued optimization problem and includes four chapters,the main contents are as follows:In chapter 1,we introduce the background and significance of this thesisIn chapter 2,we explain some required preliminaries on improvement sets and quasi-relative interior.In chapter 3,we study optimality conditions of E-Benson proper efficient element for nonconvex set-valued optimization problems.Firstly,an equivalent characterization that a set is nearly E-subconvexlike is given.Then,Lagrange multiplier theorem of E-Benson proper efficient element of nearly E-subconvexlike set-valued optimization under the condition of cone with compact base or weak compact base is obtained.At last.E-saddle points theorem for set-valued optimization problems is presentedIn chapter 4,we present optimality conditions of weakly efficient element for non-convex set-valued optimization problems based on quasi-relative interior.Firstly,the relationship between weakly efficient element and linear subspace is discussed,by using separation theorem involving the quasi-relative interior,optimality conditions of weak-ly efficient element is obtained.Then,Lagrange multiplier theorem of weakly efficient element based on quasi-relative interior is presented.