Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2005-007 (July 19, 2005)

Robust Solution of Monotone Stochastic Linear Complementarity Problems
by Xiaojun Chen, Chao Zhang and Masao Fukushima

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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. Moreover, by way of a regularization technique, we prove that the solvability of the EV formulation implies the solvability of the ERM formulation. 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 results are given to illustrate the characteristics of the solutions.