Set-valued minimax programming problems under $ \sigma $-arcwisely connectivity

Koushik Das; Savin Treanţă; Thongchai Botmart; Koushik Das; Savin Treanţă; Thongchai Botmart

doi:10.3934/math.2023569

AIMS Mathematics

2023, Volume 8, Issue 5: 11238-11258. doi: 10.3934/math.2023569

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Set-valued minimax programming problems under $ \sigma $-arcwisely connectivity

1.
Department of Mathematics, Taki Government College, Taki 743429, India
2.
Department of Applied Mathematics, University Politehnica of Bucharest, Bucharest 060042, Romania
3.
Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania
4.
"Fundamental Sciences Applied in Engineering" Research Center (SFAI), University Politehnica of Bucharest, Bucharest 060042, Romania
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khoon Kaen 40002, Thailand

Received: 30 August 2022 Revised: 04 December 2022 Accepted: 10 January 2023 Published: 09 March 2023
MSC : 26B25, 49N15

A set-valued minimax programming problem (in short, SVMP) is taken into consideration in this study. We present the idea of $ \sigma $-arcwisely connectivity of set-valued maps (in short, SVM) in the broader sense of arcwisely connected SVMs. The sufficient criteria for Karush-Kuhn-Tucker (KKT) optimality are constituted for the problem (MP) under contingent epidifferentiation and $ \sigma $-arcwisely connectivity suppositions. In addition, we develop the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) kinds models of duality and verify the associated strong, weak, and converse theorems of duality among the primal (MP) and the associated figures of duals under $ \sigma $-arcwisely connectivity supposition.
- convex cone,
- contingent epidifferentiation,
- arcwisely connectivity,
- duality
Citation: Koushik Das, Savin Treanţă, Thongchai Botmart. Set-valued minimax programming problems under $ \sigma $-arcwisely connectivity[J]. AIMS Mathematics, 2023, 8(5): 11238-11258. doi: 10.3934/math.2023569

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Abstract

A set-valued minimax programming problem (in short, SVMP) is taken into consideration in this study. We present the idea of $ \sigma $-arcwisely connectivity of set-valued maps (in short, SVM) in the broader sense of arcwisely connected SVMs. The sufficient criteria for Karush-Kuhn-Tucker (KKT) optimality are constituted for the problem (MP) under contingent epidifferentiation and $ \sigma $-arcwisely connectivity suppositions. In addition, we develop the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) kinds models of duality and verify the associated strong, weak, and converse theorems of duality among the primal (MP) and the associated figures of duals under $ \sigma $-arcwisely connectivity supposition.

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