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

<p>In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.</p>
</abstract>

In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.

Second-order optimality conditions in nonsmooth vector optimization

Atma Ram Sanatan Dharma College, University of Delhi

Control and Cybernetics

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

{"article-title":"Second-order optimality conditions in nonsmooth vector optimization"}

In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order...

Second-order optimality conditions in nonsmooth vector optimization

Published Online: Feb 24, 2024

Page range: 35 - 51

Received: Aug 01, 2021

Accepted: Sep 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0031

Keywords
vector optimization, cones, nonsmooth second-order cone-convexity, second-order optimality, duality

© 2023 Priyanka Yadav, published by Sciendo

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

Second-order optimality conditions in nonsmooth vector optimization

Published Online: Feb 24, 2024

Page range: 35 - 51

Received: Aug 01, 2021

Accepted: Sep 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0031

Keywordsvector optimization, cones, nonsmooth second-order cone-convexity, second-order optimality, duality

© 2023 Priyanka Yadav, published by Sciendo

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

Keywords
vector optimization, cones, nonsmooth second-order cone-convexity, second-order optimality, duality