, Volume 117, Issue 1, pp 5180
First online:
Robust solution of monotone stochastic linear complementarity problems
 Xiaojun ChenAffiliated withDepartment of Mathematical Sciences, Faculty of Science and Technology, Hirosaki University
 , Chao ZhangAffiliated withDepartment of Mathematical Sciences, Faculty of Science and Technology, Hirosaki University
 , Masao FukushimaAffiliated withDepartment of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University Email author
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We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semidefinite. 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 semidefinite 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 minimizationMathematics Subject Classification (2000)
90C15 90C33 Title
 Robust solution of monotone stochastic linear complementarity problems
 Journal

Mathematical Programming
Volume 117, Issue 12 , pp 5180
 Cover Date
 200903
 DOI
 10.1007/s101070070163z
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Stochastic linear complementarity problem
 NCP function
 Expected residual minimization
 90C15
 90C33
 Industry Sectors
 Authors

 Xiaojun Chen ^{(1)}
 Chao Zhang ^{(1)}
 Masao Fukushima ^{(2)}
 Author Affiliations

 1. Department of Mathematical Sciences, Faculty of Science and Technology, Hirosaki University, Hirosaki, 0368561, Japan
 2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 6068501, Japan