Set-valued parametric optimization problems with higher-order \(\rho \)-cone arcwise connectedness

In this study, we take into account the set-valued parametric optimization problem (PP) (abbreviated as SVPOP), in which both the objective and constraint maps are set-valued. In order to generalize higher-order cone arcwise connected set-valued maps, we develop the idea of higher-order \(\rho \) $\rho$ -cone arcwise connectedness of set-valued maps. Under higher-order contingent epiderivative and higher-order \(\rho \) $\rho$ -cone arcwise connectivity assumptions, we provide higher-order sufficient Karush-Kuhn-Tucker (KKT) optimality criteria for the problem (PP). In addition, we investigate higher-order Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and establish the corresponding higher-order weak, strong, and converse duality theorems between the primal problem (PP) and analogous dual problems under the presumption of higher-order \(\rho \) $\rho$ -cone arcwise connectedness.