Mathematical Programming

, Volume 117, Issue 1, pp 51–80

Robust solution of monotone stochastic linear complementarity problems

FULL LENGTH PAPER

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 

Mathematics Subject Classification (2000)

90C15 90C33 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Faculty of Science and TechnologyHirosaki UniversityHirosakiJapan
  2. 2.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan

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