Asymptotic Analysis for One-Stage Stochastic Linear Complementarity Problems and Applications

Abstract

One-stage stochastic linear complementarity problem (SLCP) is a special case of a multi-stage stochastic linear complementarity problem, which has important applications in economic engineering and operations management. In this paper, we establish asymptotic analysis results of a sample-average approximation (SAA) estimator for the SLCP. The asymptotic normality analysis results for the stochastic-constrained optimization problem are extended to the SLCP model and then the conditions, which ensure the convergence in distribution of the sample-average approximation estimator for the SLCP to multivariate normal with zero mean vector and a covariance matrix, are obtained. The results obtained are finally applied for estimating the confidence region of a solution for the SLCP.