Stochastic $R_0$ Matrix Linear Complementarity Problems

Abstract

We consider the expected residual minimization formulation of the stochastic $R_0$ matrix linear complementarity problem. We show that the involved matrix being a stochastic $R_0$ matrix is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded. Moreover, local and global error bounds are given for the stochastic $R_0$ matrix linear complementarity problem. A stochastic approximation method with acceleration by averaging is applied to solve the expected residual minimization problem. Numerical examples and applications of traffic equilibrium and system control are given.