# Robust solution of monotone stochastic linear complementarity problems

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DOI: 10.1007/s10107-007-0163-z

- Cite this article as:
- Chen, X., Zhang, C. & Fukushima, M. Math. Program. (2009) 117: 51. doi:10.1007/s10107-007-0163-z

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## Abstract

We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty and bounded solution set. We give a new error bound for the monotone LCP and use it to show that solutions of the ERM formulation are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in SLCP. Numerical examples including a stochastic traffic equilibrium problem are given to illustrate the characteristics of the solutions.