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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Veröffentlicht in:Computational optimization and applications Jg. 27; H. 3; S. 223 - 246
Hauptverfasser: Chen, Xiaojun, Fukushima, Masao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer Nature B.V 01.03.2004
Schlagworte:
Applied mathematics
Mathematical models
Mathematical programming
Neighborhoods
Studies
ISSN:0926-6003, 1573-2894
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Zusammenfassung: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]
Bibliographie:SourceType-Scholarly Journals-1
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ISSN:0926-6003
1573-2894
DOI:10.1023/B:COAP.0000013057.54647.6d