SET-VALUED MINIMAX FRACTIONAL PROGRAMMING PROBLEMS WITH HIGHER-ORDER ρ-CONE ARCWISE CONNECTEDNESS
By
Koushik Das
Department of Mathematics, Taki Government College, Taki, West Bengal, India-743429 Present : Department of Mathematics, Government General Degree College, Singur, Hooghly, West Bengal, India-712409
Email: koushikdas.maths@gmail.com
(Received: December 06, 2023; In format: December 08, 2023; Revised: June 06, 2024; Accepted: October 14, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54211
Abstract
In this study, a set-valued minimax fractional programming problem (in short, SVMFPP) (MFP) is taken into consideration, where the objective as well as constraint maps are set-valued. As a generalization of higher-order cone arcwise connected set-valued maps, we present the idea of higher-order ρ-cone arcwise connectedness. Under the higher-order ρ-cone arcwise connectedness supposition, we show the higherorder sufficient Karush-Kuhn-Tucker (KKT) requirements for the existence of minimizers of the problem (MFP).
2020 Mathematical Sciences Classification: 26B25; 49N15.
Keywords: Convex cone; Set-valued map; Contingent epiderivative; Duality; Arcwisely connectedness.