Sensitivity Analysis in Parametric Convex Vector Optimization

TL;DR

This paper develops formulas for sensitivity analysis of efficient sets in parametric convex vector optimization, using convex analysis tools to derive conditions based on problem data.

Contribution

It introduces new formulas for the Fréchet coderivative of perturbation maps in convex vector optimization, simplifying conditions due to convexity assumptions.

Findings

Formulas for computing the Fréchet coderivative of perturbation maps.

Conditions are straightforward and directly based on problem data.

Approach differs from general case by leveraging convex analysis tools.

Abstract

In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps. We establish the formulas for computing the Fr\'{e}chet coderivative of the profile of the above three kinds of perturbation maps. Because of the convexity assumptions, the conditions set are fairly simple if compared to those in the general case. In addition, our conditions are stated directly on the data of the problem. It is worth emphasizing that our approach is based on convex analysis tools which are different from those in the general case.