Partial exact penalty for mathematical programs with equilibrium constraints
type: Item
instance of: scholarly article
title: Partial exact penalty for mathematical programs with equilibrium constraints
zbMATH Open document ID: 1170.65052
author: Jane Ye
author: Jiaping Zhu
author: Guoshan Liu
published in: Set-Valued Analysis
publication date: 2009-03-16T00:00:00Z
review text: A new approach to mathematical programming with equilibrium constraints (MPEC) is proposed based on the result of partial exact penalization. An algorithm for computing the M-stationary point of MPEC without linear independence constraint qualification is elaborated. The nonsmoothness of the partial exact function is the main difficulty. The authors overcome it by smoothing the partial exact penalty function, obtaining a smooth optimization problem with simple linear complementarity non-negative constraints. Although the subproblem is still an MPEC, the complementarity constraint is simple and the linear independence constraint qualification holds at all feasible points. This makes the problem solvable by existing algorithms for finding S-stationary points. The smoothing algorithm proposed in this paper takes the smoothing parameter to zero and adjusts the partial exact penalty parameter. Its behaviour is similar to other penalty algorithms, since the accumulation point may not be feasible. However, it is proved that if the accumulation point satisfies an extended version of MPEC with general Mangasarian-Fromovitz constraint qualification then it is a Mordukhovich-stationary point.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 5529269
zbMATH Keywords: mathematical program with equilibrium constraints
zbMATH Keywords: Mangasarian-Fromovitz constraint qualification
zbMATH Keywords: partial exact penalization
zbMATH Keywords: global convergence
zbMATH Keywords: M-stationary points
zbMATH Keywords: algorithm
zbMATH Keywords: complementarity constraint
zbMATH Keywords: smoothing algorithm
zbMATH Keywords: Mordukhovich-stationary point
MaRDI profile type: Publication
full work available at URL: s11228-008-0095-7
OpenAlex ID: W1993863961
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DOI: 10.1007/S11228-008-0095-7
description: scientific article; zbMATH DE number 5529269