Stochastic second-order-cone complementarity problems: expected residual minimization formulation and its applications
Stochastic second-order-cone complementarity problems: expected residual minimization formulation and its applications
复制标题
随机二阶锥互补问题：期望残差最小化公式及其应用
DOI：
10.1007/s10107-017-1121-z
复制
发表时间：
2017
影响因子：
2.7
通讯作者：
Zhang Jin
中科院分区：
文献类型：
--
作者：
Lin Gui Hua;Luo Mei Ju;Zhang Dali;Zhang Jin
考虑一类随机二阶锥互补问题（SSOCCP），它是显式随机互补问题的推广，可以看作是某些随机二阶锥规划问题的Karush-Kuhn-Tucker条件.由于随机变量的存在，SSOCCP可能没有一个共同的解决方案，几乎每一个实现。在本文中，受随机互补问题的研究工作的启发，我们提出了一个确定性的公式称为期望残差最小化公式SSOCCP。我们提出了一种基于Monte Carlo近似技术的近似方法，并研究了与ERM方程解的存在性有关的一些性质。此外，我们还进行了一些实际应用的实验，包括随机天然气输送问题和辐射状网络的随机最优潮流问题。
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.