Generalized Second-Order Duality for a Continuous Programming Problem with Support Functions

Abstract

A generalized second-order dual is formulated for a continuous programming problem in which support functions appear in both objective and constraint functions, hence it is nondifferentiable. Under second-order pseudoinvexity and second-order quasi-invexity, various duality theorems are proved for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous programming problems with natural boundary values is constructed and it is pointed out that the duality results for the pair can be validated analogously to those of the dual models with fixed end points. Finally, a close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly mentioned.