The Distributionally Robust Optimization Reformulation for Stochastic Complementarity ProblemsReport as inadecuate

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Abstract and Applied Analysis - Volume 2014 2014, Article ID 469587, 7 pages -

Research Article

School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116025, China

College 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.


We investigate the stochastic linear complementarity problem affinelyaffected by the uncertain parameters. Assuming that we have only limitedinformation 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 complementarityproblem as a distributionally robust optimization reformation which minimizesthe worst case of an expected complementarity measure with nonnegativityconstraints and a distributionally robust joint chance constraint representingthat the probability of the linear mapping being nonnegative is not less thana given probability level. Applying the cone dual theory and S-procedure, weshow that the distributionally robust counterpart of the uncertain complementarityproblem can be conservatively approximated by the optimization withbilinear matrix inequalities. Preliminary numerical results show that a solutionof our method is desirable.

Author: Liyan Xu, Bo Yu, and Wei Liu



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