Constraint Qualifications and Gradient Flows for Block Vanishing Constraint Problems
Abstract
Mathematical Programs with Blocks of Vanishing Constraints (MP-BVCs) are a challenging class of optimization problems due to the loss of standard constraint qualifications. Based on existing theory for classical MPVCs, i.e., MPBVC with block size one, we extend the constraint qualification theory for MPBVCs and show that the known LICQ-type condition for MPBVCs implies the Guignard Constraint Qualification (GCQ). A novel piecewise gradient flow approach converges under GCQ. It directly computes strongly stationary points and is an extension of the piecewise gradient flow approach for classic MPVC problems. Numerical experiments on several truss topology design instances with two and even three applied load forces demonstrate the robustness and effectiveness of the method.
Related
- Constraint Qualifications and Regularity Conditions for Nonlinear Constraint Systems
- Variational relaxation and gradient flows for degenerate elliptic conductivity problems
- Beyond Affine Layers: Bounded Ball Coverings to Preclude Gradient Vanishing
- Vanishing discount and viscosity selection problems for mechanical Hamilton--Jacobi equations
- Homogenization of degenerate parabolic Signorini problems with vanishing storage and oscillating surface fluxes
BibTeX
@misc{niederer2026constraint,
title = {{Constraint Qualifications and Gradient Flows for Block Vanishing Constraint Problems}},
author = {Julian Niederer and Christoph Hansknecht and Andreas Potschka and Ekaterina Kostina},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20368},
eprint = {2609.20368},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20368},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraint Qualifications and Gradient Flows for Block Vanishing Constraint Problems
AU - Julian Niederer
AU - Christoph Hansknecht
AU - Andreas Potschka
AU - Ekaterina Kostina
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20368
UR - https://arxiv.org/abs/2609.20368
AB - Mathematical Programs with Blocks of Vanishing Constraints (MP-BVCs) are a challenging class of optimization problems due to the loss of standard constraint qualifications. Based on existing theory for classical MPVCs, i.e., MPBVC with block size one, we extend the constraint qualification theory for MPBVCs and show that the known LICQ-type condition for MPBVCs implies the Guignard Constraint Qualification (GCQ). A novel piecewise gradient flow approach converges under GCQ. It directly computes strongly stationary points and is an extension of the piecewise gradient flow approach for classic MPVC problems. Numerical experiments on several truss topology design instances with two and even three applied load forces demonstrate the robustness and effectiveness of the method.
ER -