Higher-order symmetric duality in nondifferentiable multi-attribute optimization over cones

Abstract

In this paper, a new pair of higher-order
nondifferentiable multiobjective symmetric dual programs over
arbitrary cones is formulated, where each of the objective functions contains a support function of a compact convex set in R^n. We identify a function lying exclusively in the class of higher-order K-η-convex and not in the class of K-η-bonvex function already existing in literature. Weak,
strong and converse duality theorems are then established under
higher-order K-η-convexity assumptions. Self duality is
obtained by assuming the functions involved to be
skew-symmetric. Several known results are also discussed as special cases.