Mathematical Programming

, Volume 117, Issue 1, pp 51–80

Robust solution of monotone stochastic linear complementarity problems


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


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.


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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