Stability and Sensitivity Analysis in Convex Vector Optimization

Tanino, T. (1986). Stability and Sensitivity Analysis in Convex Vector Optimization. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-86-015

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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 which 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 with those in the general case. Moreover, a complete characterization of the contingent derivative of the perturbation map is obtained under some assumptions. It provides a quantitative information on the behavior of the perturbation map and allows to investigate the sensitivity of the efficient set with respect to the perturbations of the problem parameters.

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