Stochastic second-order-cone complementarity problems: expected residual minimization formulation and its applications

• 成果类型: Article
• 署名作者: Lin, Gui-Hua; Luo, Mei-Ju; Zhang, Dali; Zhang, Jin
• 署名单位: Shanghai University; Liaoning University; Shanghai Jiao Tong University; Hong Kong Baptist University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1121-z
• 发表日期: 2017
• 页码: 197-233
• 关键词: mathematical programs; equilibrium constraints; optimization; networks; systems

摘要

This paper considers a class of stochastic second-order-cone complementarity problems (SSOCCP), which are generalizations of the noticeable stochastic complementarity problems and can be regarded as the Karush-Kuhn-Tucker conditions of some stochastic second-order-cone programming problems. Due to the existence of random variables, the SSOCCP may not have a common solution for almost every realization . In this paper, motivated by the works on stochastic complementarity problems, we present a deterministic formulation called the expected residual minimization formulation for SSOCCP. We present an approximation method based on the Monte Carlo approximation techniques and investigate some properties related to existence of solutions of the ERM formulation. Furthermore, we experiment some practical applications, which include a stochastic natural gas transmission problem and a stochastic optimal power flow problem in radial network.