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 t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/469587 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |