Qualitative Properties of Robust Benson Efficient Solutions of Uncertain Vector Optimization Problems

Lam Quoc Anh (), Vo Thi Mong Thuy () and Xiaopeng Zhao ()
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Lam Quoc Anh: Can Tho University
Vo Thi Mong Thuy: University of Science
Xiaopeng Zhao: Tiangong University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 1, No 19, 37 pages

Abstract: Abstract In this paper, we consider both unconstrained and constrained uncertain vector optimization problems involving free disposal sets, and study the qualitative properties of their robust Benson efficient solutions. First, we discuss necessary and sufficient optimality conditions for the robust Benson efficient solutions of these problems using the linear scalarization method. Then, by utilizing this approach, we investigate the semicontinuity properties of the solution maps when the problem data is perturbed by parameters given in parameter spaces. Finally, we suggest concepts of approximate robust Benson efficient solutions and investigate Hausdorff well-posedness conditions for such problems with respect to these approximate solutions. Several examples are provided to illustrate the applicability and novelty of the results obtained in this study.

Keywords: Uncerntain vector optimization; Optimality condition; Stability; Well-posedness; Robust Benson efficient solution; Free disposal set; Scalarization method; 49K27; 49K40; 90C31; 90C46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02638-z

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