<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

LAMA, Sidi Mohamed Ben Abdellah University

Dhar El Mahraz, Department of Mathematics

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized...

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

Published Online: Feb 24, 2024

Page range: 425 - 444

Received: May 01, 2021

Accepted: Oct 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0023

Keywords
approximations, set-valued optimization, local weak l-minimal solutions, optimality conditions

© 2022 Nazih Abderrazzak Gadhi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Feb 24, 2024

Page range: 425 - 444

Received: May 01, 2021

Accepted: Oct 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0023

Keywordsapproximations, set-valued optimization, local weak l-minimal solutions, optimality conditions

© 2022 Nazih Abderrazzak Gadhi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
approximations, set-valued optimization, local weak l-minimal solutions, optimality conditions