Correspondence between a new pair of nondifferentiable mixed dual vector programs and higher-order generalized convexity

In this paper, a new pair of higher-order nondifferentiable multiobjective mixed symmetric dual programs over arbitrary cones is formulated, where each of the objective functions contains a support function of a compact convex set. Usual duality theorems are established under higher-order K- \((F,\alpha ,\rho ,d)\) $(F,\alpha ,\rho ,d)$ -convexity assumptions. Also, the example of a higher-order dual pair, which shows that higher-order provides tighter bounds for the value of the objective function of the primal and dual problem, is given in the paper. Several known results are also discussed as special cases.