Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2003-009 (July 16, 2003)

Approximation and Convergence in Stochastic Linear Complementarity Problems
by Xiaojun Chen and Masao Fukushima

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The stochastic linear complementarity problem is formulated as a problem of minimizing an expected residual defined by an NCP function. We generate observations by the quasi-Monte Carlo methods and show that every accumulation point of minimizers of discrete approximation problems is a minimum residual solution of the stochastic linear complementarity problem. We show that a sufficient condition for the existence of a solution to the residual minimization problem and its discrete approximations is that there is an observation $\omega^i$ such that the cost matrix $M(\omega^i)$ is an $R_0$ matrix. Furthermore, we show that a class of fixed cost problems are continuously differentiable and can be solved without using discrete approximation.