The Stability Analysis Of Pseudomonotone Vector Equilibrium Problems

The stability analysis for vector equilibrium problems is an important topic in vector optimization and it is mainly to study the continuity of perturbed solution mappings. Usually, solution stability investigations were devoted to semicontinuity,Lipschitz/H?lder continuity and so on. The researches of semicontinuities to solution mappings for parametric vector equilibrium problems are very interesting. Among many approaches dealing with the semicontinuities of solution mappings for parametric vector equilibrium problems, the scalarization method is of considerable interest and effective.In the third and fourth chapters of this thesis, new semicontinuous results of the solution mappings for parametric generalized vector equilibrium problems and parametric strong vector variational inequalities are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions.On the other hand, from the computational point of view, one important research direction in vector variational inequalities is the study of gap functions and error bounds.By using gap functions, vector variational inequalities can be transformed into optimization problems; and using error bounds, we can obtain an upper estimate of the distance of an arbitrary feasible point to the solution set of the vector variational inequalities. In the fourth chapter of this thesis, the error bounds for weak vector variational inequalities are obtained in terms of the regularized gap functions within the framework of strong pseudomonotonicity assumptions.Moreover, improvement sets can unify different kinds of solution notions of vector optimization problems. In the fifth chapter of this thesis, for the generalized weak vector equilibrium problem where the ordering relation is defined via an improvement set, a linear scalarization characterization is established. By applying the obtained result, new semicontinuities of solution mappings to parametric generalized weak vector equilibrium problems are obtained, under strict pseudomonotonicity assumptions.