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Abstract and Applied Analysis
Volume 2014, Article ID 469587, 7 pages
http://dx.doi.org/10.1155/2014/469587
Research Article

The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems

Liyan Xu,1,2 Bo Yu,1 and Wei Liu1

1School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116025, China
2College of Science, Harbin Engineering University, Harbin, Heilongjiang 150001, China

Received 19 May 2014; Accepted 23 September 2014; Published 6 November 2014

Academic Editor: Victor Kovtunenko

Copyright © 2014 Liyan Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linear mapping being nonnegative is not less than a given probability level. Applying the cone dual theory and S-procedure, we show that the distributionally robust counterpart of the uncertain complementarity problem can be conservatively approximated by the optimization with bilinear matrix inequalities. Preliminary numerical results show that a solution of our method is desirable.