Asymptotic Analysis for a Stochastic Second-Order Cone Programming and Applications

Abstract

Stochastic second-order cone programming (SSOCP) is an extension of deterministic second-order cone programming, which demonstrates underlying uncertainties in practical problems arising in economics engineering and operations management. In this paper, asymptotic analysis of sample average approximation estimator for SSOCP is established. Conditions ensuring the asymptotic normality of sample average approximation estimators for SSOCP are obtained and the corresponding covariance matrix is described in a closed form. Based on the analysis, the method to estimate the confidence region of a stationary point of SSOCP is provided and three examples are illustrated to show the applications of the method.