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Stochastic R 0 matrix linear complementarity problems. (English) Zbl 1151.90052

The authors consider the expected residual minimization method (ERM) for solving stochastic linear complementarity problems

x0,M(ω)x+q(ω)0,x T (M(ω)x+q(ω))=0·

This problem is transformed to a minimization problem minG(x)s.t.x0. The study is based on the concept of stochastic R 0 matrices. It is shown, that the ERM problem is solvable for any q(·) if and only if M(·) is a stochastic R 0 matrix. The differentiability of G(x) is analysed under a certain strict complementarity condition with probability one. Necessary an sufficient optimality conditions for a solution x ¯ are given together with error bounds. Finally the authors report on experiments for solving ERM numerically. The stochastic complementarity concept is applied to a traffic equilibrium flow and a control problem.

MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C15Stochastic programming