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

Shuang Lin, Jie Zhang () and Chen Qiu
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Shuang Lin: Department of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, China
Jie Zhang: School of Mathematics, Liaoning Normal University, Dalian 116029, China
Chen Qiu: School of Mathematics, Liaoning Normal University, Dalian 116029, China

Mathematics, 2023, vol. 11, issue 2, 1-14

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.

Keywords: stochastic linear complementarity problem; asymptotic analysis; sample-average approximation; convergence in distribution; confidence regions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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