Abstract and Applied Analysis

The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems

Liyan Xu, Bo Yu, and Wei Liu

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 469587, 7 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049859

Digital Object Identifier
doi:10.1155/2014/469587

Mathematical Reviews number (MathSciNet)
MR3278342

Zentralblatt MATH identifier
07022438

Citation

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


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