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Expected residual minimization method for stochastic linear complementarity problems. (English) Zbl 1162.90527
Summary: This paper presents a new formulation for the stochastic linear complementarity problem (SLCP), which aims at minimizing an expected residual defined by an NCP function. We generate observations by the quasi-Monte Carlo methods and prove that every accumulation point of minimizers of discrete approximation problems is a minimum expected residual solution of the SLCP. We show that a sufficient condition for the existence of a solution to the expected residual minimization (ERM) problem and its discrete approximations is that there is an observation omega${}^{i}$ such that the coefficient matrix $M$(omega${}^{i}$) is an ${R}_{0}$ matrix. Furthermore, we show that, for a class of problems with fixed coefficient matrices, the ERM problem becomes continuously differentiable and can be solved without using discrete approximation. Preliminary numerical results on a refinery production problem indicate that a solution of the new formulation is desirable.

##### MSC:
 90C15 Stochastic programming 90C33 Complementarity and equilibrium problems; variational inequalities (finite dimensions)