Work

Optimality conditions for global minimizers to a class of convex set optimization problem subjected to geometric constraints

Year: 2025

Type: article

Abstract: In this paper, we study optimality conditions for both global and approximate minimizers to convex set optimization problems with geometric constraints. We first consider a form of Gerstewitz’s nonlinear scalarization function concerning the set-less relation introduced by Kuroiwa. Then, it is employed to construct a type of directional derivative and sub-gradient for cone-convex set-valued maps. We also give some properties and usual calculus rules for these concepts. Later, some necessary and sufficient conditions for global and approximate solutions are established. Examples are provided for analyzing and illustrating the obtained results.

Source: RAIRO - Operations Research

DOI: 10.1051/ro/2025025

Authors: Minh Tung Nguyen, Thanh Duoc Pham, Van Hoi Nguyen

Institutions: Ho Chi Minh University of Banking, Trường Đại học Kỹ thuật - Công nghệ Cần Thơ, Vietnam National University Ho Chi Minh City, University of Information Technology

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Vietnam Institute for Advanced Study in Mathematics

OpenAlex ID: W4407964986