Department of Mathematics
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.
SSOCCP, ERM formulation, Monte Carlo approximation, Natural gas transmission, Optimal power flow
Source Publication Title
The final publication is available at Springer via http://dx.doi.org/10.1007/s10107-017-1121-z
This work was supported in part by NSFC (Nos. 11431004, 11501275, 71501127, 11671250, 11601458), Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034), Scientific Research Fund of Liaoning Provincial Education Department (No. L2015199), and Hong Kong Baptist University FRG1/15-16/027.
Link to Publisher's Edition
Lin, G., Luo, M., Zhang, D., & Zhang, J. (2017). Stochastic second-order-cone complementarity problems: Expected residual minimization formulation and its applications. Mathematical Programming, 165 (1), 197-233. https://doi.org/10.1007/s10107-017-1121-z