Robust solution of monotone stochastic linear complementarity problems Authors Xiaojun Chen Department of Mathematical Sciences, Faculty of Science and Technology Hirosaki University Chao Zhang Department of Mathematical Sciences, Faculty of Science and Technology Hirosaki University Masao Fukushima Department of Applied Mathematics and Physics, Graduate School of Informatics Kyoto University FULL LENGTH PAPER

First Online: 18 July 2007 Received: 19 July 2005 Accepted: 19 June 2006 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
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.

Keywords Stochastic linear complementarity problem NCP function Expected residual minimization It is our great pleasure and honor to dedicate this paper to Professor Steve Robinson on the occasion of his 65th birthday. His original ideas and deep insight have always been so inspiring and beneficial to our work. This paper is just one of such instances.

This work was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the
Promotion of Science.

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