Asymptotic Analysis for a Stochastic Second-Order Cone Programming and Applications
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Published:2021-11-06
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Volume:
Page:
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ISSN:0217-5959
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Container-title:Asia-Pacific Journal of Operational Research
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language:en
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Short-container-title:Asia Pac. J. Oper. Res.
Author:
Zhang Jie1,
Shi Yue1,
Tong Mengmeng2,
Li Siying1
Affiliation:
1. School of Mathematics, Liaoning Normal, University, Dalian 116029, P. R. China
2. School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, P. R. China
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.
Funder
National Natural Science Foundation of China
Liaoning Revitalization Talents Program
Scientific Research Fund of Liaoning Provincial Education Department
Natural Science Foundation of Liaoning Province
Publisher
World Scientific Pub Co Pte Ltd
Subject
Management Science and Operations Research,Management Science and Operations Research