Sensitivity Analysis in Parametrized Convex Vector Optimization

Abstract

This paper provides some results concerning sensitivity analysis in parametrized convex vector optimization. We consider three types of perturbation maps (i.e., perturbation map, proper perturbation map, and weak perturbation map) according to three kinds of solution concepts (i.e., minimality, proper minimality, and weak minimality with respect to a fixed ordering cone) for a vector optimization problem. As for general vector optimization, authors have already established the behavior of the above three types of perturbation maps by using the concept of contingent derivatives for set-valued maps in finite dimensional Euclidean spaces. In this paper we concentrate on convex vector optimization and provide quantitative properties of the perturbation maps under some convexity assumptions. Namely, we investigate the relationships between the contingent derivatives of the perturbation maps and those of the feasible set map in the objective space.