KINDS OF VECTOR INVEX

Abstract

Necessary Lagrangian conditions for a constrained minimum become sufficient under generalized convex assumptions, in particular invex, and duality results follow. Many classes of vector functions with properties related to invex have been studied, but It has not been clear how far these classes are distinct. Various inclusions between these classes are now established Some modifications of invex can be regarded as perturbations of invex. There is a stability criterion for when the invex property is preserved under small perturbations. Some results extend to nondifferentiable (Lipschitz) functions.