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
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.