Sensitivity Analysis in Parametric Convex Vector Optimization

2023/06/12 by Duong Thi Viet An, Lê Thanh Tùng, An, Duong Thi Viet +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2306.06947

openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Fréchet 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.

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