<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

Publié en ligne: 24 févr. 2024

Pages: 425 - 444

Reçu: 01 mai 2021

Accepté: 01 oct. 2022

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

Mots clés
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

Publié en ligne: 24 févr. 2024

Pages: 425 - 444

Reçu: 01 mai 2021

Accepté: 01 oct. 2022

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

Mots clésapproximations, 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.

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