Block-Structured MPBVC Reformulation as an MPCC

Determine how to reformulate the block structure of mathematical programs with blocks of vanishing constraints (MPBVCs) as mathematical programs with complementarity constraints (MPCCs) without increasing the problem size or introducing additional stationarity concepts.

Background

Mathematical programs with blocks of vanishing constraints generalize mathematical programs with vanishing constraints by allowing one controlling constraint to govern multiple vanishing constraints. Although mathematical programs with complementarity constraints encompass related vanishing-constraint problem classes, the block structure of MPBVCs does not have an established equivalent MPCC formulation.

A successful reformulation would enable the use of established MPCC solution strategies while preserving the original problem dimension and avoiding the need for additional stationarity notions. The paper does not resolve this reformulation issue and instead develops constraint qualifications and a gradient-flow method directly for MPBVCs.