Study On The Stability Of Vector Optimization Problems And Its Related Problems Via General Ordering Sets

In this thesis,we discuss the stability of solutions for generalized perturbed vector quasi-equilibrium problems via free disposal sets,perturbed set-valued optimization problems with approximate quasi-equilibrium constraints under general ordering sets,perturbed symmetric set-valued quasi-equilibrium problems via improvement sets and parametric strong symmetric quasi-equilibrium problems,including the Painlevé-Kuratowski convergence of solution sets and the Berge-semicontinuity of solution mappings.This thesis is divided into seven chapters.The main work and innovation include the following aspects:1.We discuss the stability of generalized perturbed vector quasi-equilibrium problems where the ordering relations are defined by free disposal set.Under some types of continuity assumption,the sufficient conditions of the Berge upper semicontinuity and the upper Painlevé-Kuratowski convergence of solutions for this problem are talked about.At the same time,by virtue of the suitable gap functions,sufficient and necessary conditions of the Berge lower semicontinuity and the lower Painlevé-Kuratowski convergence of solutions are obtained.Our results extend and improve the corresponding ones in [44,52,53].2.The perturbed set-valued optimization problem with approximate quasiequilibrium constraints are discussed under general ordering sets.Firstly,we study the Painlevé-Kuratowski convergence of constraint sets by using some weaker assumptions.Then,under some types of convergence assumption,the sufficient conditions of upper(lower)Painlevé-Kuratowski convergence of -minimal point sets,-weak minimal point sets and -Borwein proper minimal point sets for the problem are obtained.3.By using a new nonlinear scalarization technique,the sufficient conditions of Berge semicontinuity of solution mappings for scalar parametric strong symmetric quasi-equilibrium problem are discussed without the assumption of monotonicity.According to the relationship between the original problem and the scalar problem,the sufficient conditions of Berge semicontinuity for solution mappings are obtained.4.The Painlevé-Kuratowski convergence of efficient solution sets for perturbed symmetric set-valued quasi-equilibrium problems are discussed by using a suitable nonlinear scalarization method.Then,under the weaker assumptions,the Painlevé-Kuratowski convergence of weak efficient solution sets for the problem is obtained.What's more,with suitable convergence assumptions,we also establish the sufficient conditions of lower Painlevé-Kuratowski convergence for Borwein proper efficient solution sets.The results extend the known ones in the literature([49–51]).