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

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.