Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators

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...

Full description

Bibliographic Details
Published in:Axioms
Main Authors: Ram Narayan Mohapatra, Prachi Sachan, Vivek Laha
Format: Article
Language:English
Published: MDPI AG 2024-07-01
Subjects:
mathematical programs with vanishing constraints
directional convexificators
optimality conditions
constraint qualifications
generalized convexity
Online Access:https://www.mdpi.com/2075-1680/13/8/516
Description
Summary: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.
ISSN:2075-1680

Similar Items