Abstract
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