Higher-order duality for a class of nondifferentiable multiobjective programming problems involving generalized type I and related functions

Abstract

This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi(2000) to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper. A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.