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Zbl 1165.90012
Chen, Xiaojun; Zhang, Chao; Fukushima, Masao
Robust solution of monotone stochastic linear complementarity problems. (English)
[J] Math. Program. 117, No. 1-2 (B), 51-80 (2009). ISSN 0025-5610; ISSN 1436-4646/e

Summary: 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.

MSC 2000:: *90C15 Stochastic programming
90C33 Complementarity problems

Keywords: stochastic linear complementarity problem; NCP function; expected residual minimization

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