A Flow-based Method for Problems with Vanishing Constraints

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.