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

Jie Zhang, Yue Shi (), Mengmeng Tong () and Siying Li ()
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Jie Zhang: School of Mathematics, Liaoning Normal, University, Dalian 116029, P. R. China
Yue Shi: School of Mathematics, Liaoning Normal, University, Dalian 116029, P. R. China
Mengmeng Tong: School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, P. R. China
Siying Li: School of Mathematics, Liaoning Normal, University, Dalian 116029, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2022, vol. 39, issue 06, 1-25

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.

Keywords: Stochastic second-order cone programming; asymptotic analysis; sample average approximation; convergence in distribution; confidence regions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0217595922500026

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