Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators-Reference-Cited by-同舟云学术

Optimality Conditions for Mathematical Programs with Vanishing Constraints Using Directional Convexificators

Published:2024-07-30 Issue:8 Volume:13 Page:516
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Mohapatra Ram Narayan¹^ORCID,Sachan Prachi²^ORCID,Laha Vivek²^ORCID

Affiliation:

1. Department of Mathematics, University of Central Florida, Orlando, FL 10587, USA

2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

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.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/8/516/pdf

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