Optimality conditions in set-valued optimization using approximations as generalized derivatives

Nazih Abderrazzak Gadhi; Aissam Ichatouhane

doi:10.2478/candc-2022-0023

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Optimality conditions in set-valued optimization using approximations as generalized derivatives

Control and Cybernetics

Volume 51 (2022): Issue 4 (December 2022)

By: Nazih Abderrazzak Gadhi and Aissam Ichatouhane

Open Access

|Feb 2024

Abstract

The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized derivatives of set-valued mappings, we establish necessary optimality conditions for a constrained set-valued optimization problem in the sense of set optimization in terms of asymptotical pointwise compact approximations. Sufficient optimality conditions are then obtained through first-order strong approximations of data set-valued mappings.

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Articles in this issue

DOI: https://doi.org/10.2478/candc-2022-0023 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

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Language: English

Page range: 425 - 444

Submitted on: May 1, 2021

Accepted on: Oct 1, 2022

Published on: Feb 24, 2024

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

approximations,

set-valued optimization,

local weak l-minimal solutions,

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

© 2024 Nazih Abderrazzak Gadhi, Aissam Ichatouhane, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 51 (2022): Issue 4 (December 2022)