Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators

Abstract

This article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also derive sufficient conditions for global optimality for the MPVC under convexity utilizing directional convexificators. Further, we introduce a Wolfe-type dual model in terms of directional convexificators and derive duality results. The results are well illustrated by examples.

Keywords

• mathematical programs with vanishing constraints
• directional convexificators
• optimality conditions
• constraint qualifications
• generalized convexity