Solutions of Parametric Set-Valued Optimization Problems of Higher-Order

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We deal with a parametric set-valued optimization problem (in brief, PSOP), where set-valued functions (in brief, SVFs) are used for the constraint and objective functions. We use the idea of higher-order p-cone convexity of SVFs (introduced by Das and Nahak [1] as a generalization of cone convex SVFs. We provide the Karush-Kuhn-Tucker (in brief, KKT) criteria of sufficiency for the presence of the minimizers of the PSOPs under higher-order p- cone convexity assumption. Further, we constitute the duality models of Mond-Weir kind and demonstrate the strong, weak, and converse duality theorems under higher-order contingent epi-derivative and higher-order p-cone convexity assumption to a couple of set-valued optimization problems (in brief, SOPs). We provide some examples to justify our results. As a special case, our results reduce to the existing ones of scalar-valued parametric optimization problems