A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints

We consider a mathematical program whose constraints involve a parametric P-matrix linear complementarity problem with the design (upper level) variables as parameters. Solutions of this complementarity problem define a piecewise linear function of the parameters. We study a smoothing function of th...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 27; no. 3; pp. 223 - 246
Main Authors: Chen, Xiaojun, Fukushima, Masao
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.03.2004
Subjects:
Applied mathematics
Mathematical models
Mathematical programming
Neighborhoods
Studies
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:We consider a mathematical program whose constraints involve a parametric P-matrix linear complementarity problem with the design (upper level) variables as parameters. Solutions of this complementarity problem define a piecewise linear function of the parameters. We study a smoothing function of this function for solving the mathematical program. We investigate the limiting behaviour of optimal solutions, KKT points and B-stationary points of the smoothing problem. We show that a class of mathematical programs with P-matrix linear complementarity constraints can be reformulated as a piecewise convex program and solved through a sequence of continuously differentiable convex programs. Preliminary numerical results indicate that the method and convex reformulation are promising. [PUBLICATION ABSTRACT]
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ISSN:0926-6003
1573-2894
DOI:10.1023/B:COAP.0000013057.54647.6d