Optimality conditions for ε-weak local quasi-efficient solutions of D.C. vector optimization problems

Nazih Abderrazzak Gadhi; Imad Amrani Zerrifi

doi:10.2478/candc-2025-0010

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Optimality conditions for ε-weak local quasi-efficient solutions of D.C. vector optimization problems

Control and Cybernetics

Volume 54 (2025): Issue 3 (September 2025)

By: Nazih Abderrazzak Gadhi and Imad Amrani Zerrifi

Open Access

|Jan 2026

Abstract

In this paper, we address a non-convex vector optimization problem, in which the objective function and constraints are defined as differences of convex vector-valued maps. By employing a separation argument, we derive necessary optimality conditions, expressed in terms of ε-regularized subdifferentials, for a point to be an ε-weak local quasi-efficient solution. To ensure the paper is self-contained, we also present sufficient optimality conditions and provide examples to illustrate the results.

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Articles in this issue

DOI: https://doi.org/10.2478/candc-2025-0010 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

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Language: English

Page range: 289 - 308

Submitted on: Sep 1, 2024

Accepted on: Nov 1, 2025

Published on: Jan 22, 2026

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

D.C. mappings (difference-of-convex-mappings),

ε-weak quasi-efficient solutions,

ε-regularized subdifferentials,

optimality conditions

Related subjects:

Computer sciences,

Computer sciences, other,

Engineering,

Electrical engineering,

Fundamentals of electrical engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Mathematics,

General mathematics

© 2026 Nazih Abderrazzak Gadhi, Imad Amrani Zerrifi, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 54 (2025): Issue 3 (September 2025)