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

<p>In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of <italic>ρ-</italic>cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under <italic>ρ</italic>-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under <italic>ρ</italic>-cone arcwise connectedness assumption.</p>
</abstract>

In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ-cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.

Set-valued minimax fractional programming problems under <italic>ρ</italic>-cone arcwise connectedness

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Set-valued minimax fractional programming problems under -cone arcwise connectedness

In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We...

Set-valued minimax fractional programming problems under ρ-cone arcwise connectedness

Published Online: Aug 12, 2022

Page range: 43 - 69

Received: Oct 01, 2021

Accepted: Jan 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0004

Keywords
convex cone, set-valued map, contingent epiderivative, arcwise connectedness, duality

© 2022 Koushik Das, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Set-valued minimax fractional programming problems under ρ-cone arcwise connectedness

Published Online: Aug 12, 2022

Page range: 43 - 69

Received: Oct 01, 2021

Accepted: Jan 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0004

Keywordsconvex cone, set-valued map, contingent epiderivative, arcwise connectedness, duality

© 2022 Koushik Das, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
convex cone, set-valued map, contingent epiderivative, arcwise connectedness, duality