<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

Publicado en línea: 12 ago 2022

Páginas: 43 - 69

Recibido: 01 oct 2021

Aceptado: 01 ene 2022

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

Palabras clave
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

Publicado en línea: 12 ago 2022

Páginas: 43 - 69

Recibido: 01 oct 2021

Aceptado: 01 ene 2022

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

Palabras claveconvex 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.

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