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Robust solutions to uncertain linear complementarity problems

Robust solutions to uncertain linear complementarity problems In this paper, we adopt the robust optimization method to consider linear complementarity problems in which the data is not specified exactly or is uncertain, and it is only known to belong to a prescribed uncertainty set. We propose the notion of the ρ-robust counterpart and the ρ-robust solution of uncertain linear complementarity problems. We discuss uncertain linear complementarity problems with three different uncertainty sets, respectively, including an unknown-but-bounded uncertainty set, an ellipsoidal uncertainty set and an intersection-of-ellipsoids uncertainty set, and present some sufficient and necessary (or sufficient) conditions which ρ-robust solutions satisfy. Some special cases are investigated in this paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Robust solutions to uncertain linear complementarity problems

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-010-0033-y
Publisher site
See Article on Publisher Site

Abstract

In this paper, we adopt the robust optimization method to consider linear complementarity problems in which the data is not specified exactly or is uncertain, and it is only known to belong to a prescribed uncertainty set. We propose the notion of the ρ-robust counterpart and the ρ-robust solution of uncertain linear complementarity problems. We discuss uncertain linear complementarity problems with three different uncertainty sets, respectively, including an unknown-but-bounded uncertainty set, an ellipsoidal uncertainty set and an intersection-of-ellipsoids uncertainty set, and present some sufficient and necessary (or sufficient) conditions which ρ-robust solutions satisfy. Some special cases are investigated in this paper.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Sep 27, 2010

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