A Flow-based Method for Problems with Vanishing Constraints

TL;DR

This paper introduces a novel flow-based method for solving Mathematical Programs with Vanishing Constraints, addressing the challenges of existing relaxation techniques by providing a more automated approach to find stationary points.

Contribution

The paper presents a new piecewise gradient flow approach for MPVCs that avoids manual tuning required by traditional relaxation methods.

Findings

Effective on real-world MPVC instances

Outperforms common relaxation approaches

Achieves first-order stationary points efficiently

Abstract

Mathematical Programs with Vanishing Constraints (MPVCs) are a notoriously challenging class of problems owing to their lack of constraint qualification. Therefore, to tackle these problems, relaxation-based approaches are typically used. While often yielding satisfactory results, they generally require significant manual tuning and adjustment of the relaxation parameter. To circumvent these problems, we introduce a novel approach based on piecewise gradient flows leading to first-order stationary points. We demonstrate the effectiveness of our method on several real-world MPVC instances and compare it to a common relaxation approach.