Robust solution of monotone stochastic linear complementarity problems

Xiaojun Chen, Chao Zhang, Masao Fukushima

Research output: Journal article publicationJournal articleAcademic researchpeer-review

105 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)51-80
Number of pages30
JournalMathematical Programming
Issue number1-2
Publication statusPublished - 1 Mar 2009
Externally publishedYes


  • Expected residual minimization
  • NCP function
  • Stochastic linear complementarity problem

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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