On an Exact Penalty Result and New Constraint Qualifications for Mathematical Programs with Vanishing Constraints

TL;DR

This paper introduces a new, weaker constraint qualification for MPVC that ensures the exactness of a tailored penalty function, improving theoretical understanding and solution methods for these complex optimization problems.

Contribution

It establishes a novel, weaker constraint qualification for MPVC that guarantees the exactness of a specific penalty function, advancing the theoretical framework.

Findings

The MPVC-tailored penalty function remains exact under the new constraint qualification.

The new constraint qualification is strictly stronger than the MPVC-Abadie qualification.

The results improve the theoretical foundation for solving MPVC problems.

Abstract

In this paper, the mathematical programs with vanishing constraints or MPVC are considered. We prove that an MPVC-tailored penalty function, introduced in [5], is still exact under a very weak and new constraint qualification. Most importantly, this constraint qualification is shown to be strictly stronger than MPVC-Abadie constraint qualification.