Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014 (2014), Article ID 469587, 7 pages.
The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems
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.
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 469587, 7 pages.
First available in Project Euclid: 27 February 2015
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Xu, Liyan; Yu, Bo; Liu, Wei. The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems. Abstr. Appl. Anal. 2014 (2014), Article ID 469587, 7 pages. doi:10.1155/2014/469587. https://projecteuclid.org/euclid.aaa/1425049859