Piecewise M-Stationarity and Related Algorithms for Mathematical Programs with Complementarity Constraints

Fuente: arXiv
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Auteurs principaux: Wang, Kexin, Biegler, Lorenz T.
Format: Preprint
Publié: 2026
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author Wang, Kexin
Biegler, Lorenz T.
author_facet Wang, Kexin
Biegler, Lorenz T.
contents This study explores B-stationarity of mathematical programs with complementarity constraints (MPCCs) and convergence behavior of MPCC algorithms. Special attention is given to the cases with biactive complementarity constraints. First, we propose the concept of piecewise M-stationarity and prove its equivalence to B-stationarity under MPCC-ACQ. Then, we investigate convergence properties of the NCP-based bounding methods we proposed in [31], without requiring MPCC-LICQ; an interpretation of the algorithm's behavior together with the concept of piecewise M-stationarity leads to a cost reduction in B-stationarity verification. In addition, practical issues related to convergence to non-strongly stationary solutions are discussed, which shows that the NCP-based complementarity reformulations have an advantage in avoiding unbounded multipliers near these solutions.
format Preprint
id arxiv_https___arxiv_org_abs_2603_23389
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Piecewise M-Stationarity and Related Algorithms for Mathematical Programs with Complementarity Constraints
Wang, Kexin
Biegler, Lorenz T.
Optimization and Control
This study explores B-stationarity of mathematical programs with complementarity constraints (MPCCs) and convergence behavior of MPCC algorithms. Special attention is given to the cases with biactive complementarity constraints. First, we propose the concept of piecewise M-stationarity and prove its equivalence to B-stationarity under MPCC-ACQ. Then, we investigate convergence properties of the NCP-based bounding methods we proposed in [31], without requiring MPCC-LICQ; an interpretation of the algorithm's behavior together with the concept of piecewise M-stationarity leads to a cost reduction in B-stationarity verification. In addition, practical issues related to convergence to non-strongly stationary solutions are discussed, which shows that the NCP-based complementarity reformulations have an advantage in avoiding unbounded multipliers near these solutions.
title Piecewise M-Stationarity and Related Algorithms for Mathematical Programs with Complementarity Constraints
topic Optimization and Control
url https://arxiv.org/abs/2603.23389