Stability and Sensitivity Analysis in Convex Vector Optimization

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Abstract

In this paper stability and sensitivity of the efficient set in convex vector optimization are considered. The perturbation map is defined as a set-valued map. It associates with each parameter vector the set of all minimal points of the parametrized feasible set with respect to an ordering cone in the objective space. Sufficient conditions for the upper and lower semicontinuity of the perturbation map are obtained. Because of the convexity assumptions, the conditions obtained are fairly simple if compared to those in the general case. Moreover, a complete characterization of the contingent derivative of the perturbation map is obtained under some assumptions. It provides quantitative information on the behavior of the perturbation map.

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