Stability, Well-posedness And Sensitivity Analysis For Vector Equilibrium Problems

This article is divided into three parts.In the first part, sensitivity anlysis for vector equilibrium is studied. We investigate differential properties of a class of set-valued maps and gap functions involving vector equilibrium. Relationships between their contingent derivatives is discussed. A formula computing contingent derivative of the gap functions is established. Optimality conditions of solutions for vector equilibriums are obtained.In the second part, it investigates stability of weak efficient solutions and strong efficient solutions for vector equilibrium problems under four kinds of perturbed conditions respectively:feasible set perturbs and vector valued map does not perturb, feasible set and vector-valued map perturb together, feasible set perturbs and set-valued map does not perturb, feasible set and set-valued map perturb together.Finally, it gives the concepts of M-well-posedness and B-well-posedness for parametric vector equilibrium problems in real Hausdorff topological vector spaces, and disscuses the relationship between them. Further, sufficient conditions for M-well-posedness and B-well-posedness are obtained.