On Constraint Qualifications for MPECs with Applications to Bilevel Hyperparameter Optimization for Machine Learning

Fuente: arXiv
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Autores principales: Li, Jiani, Li, Qingna, Zemkoho, Alain
Formato: Preprint
Publicado: 2025
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author Li, Jiani
Li, Qingna
Zemkoho, Alain
author_facet Li, Jiani
Li, Qingna
Zemkoho, Alain
contents Constraint qualifications for a Mathematical Program with Equilibrium Constraints (MPEC) are essential for analyzing stationarity properties and establishing convergence results. In this paper, we explore several classical MPEC constraint qualifications and clarify the relationships among them. We subsequently examine the behavior of these constraint qualifications in the context of a specific MPEC derived from bilevel hyperparameter optimization (BHO) for L1-loss support vector classification. In particular, for such an MPEC, we provide a complete characterization of the well-known MPEC linear independence constraint qualification (MPEC-LICQ), therefore, establishing conditions under which it holds or fails for our BHO for support vector machines.
format Preprint
id arxiv_https___arxiv_org_abs_2508_12850
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Constraint Qualifications for MPECs with Applications to Bilevel Hyperparameter Optimization for Machine Learning
Li, Jiani
Li, Qingna
Zemkoho, Alain
Optimization and Control
90C33, 90C30, 90C46
Constraint qualifications for a Mathematical Program with Equilibrium Constraints (MPEC) are essential for analyzing stationarity properties and establishing convergence results. In this paper, we explore several classical MPEC constraint qualifications and clarify the relationships among them. We subsequently examine the behavior of these constraint qualifications in the context of a specific MPEC derived from bilevel hyperparameter optimization (BHO) for L1-loss support vector classification. In particular, for such an MPEC, we provide a complete characterization of the well-known MPEC linear independence constraint qualification (MPEC-LICQ), therefore, establishing conditions under which it holds or fails for our BHO for support vector machines.
title On Constraint Qualifications for MPECs with Applications to Bilevel Hyperparameter Optimization for Machine Learning
topic Optimization and Control
90C33, 90C30, 90C46
url https://arxiv.org/abs/2508.12850