TY - JOUR
T1 - Stochastic second-order-cone complementarity problems
T2 - expected residual minimization formulation and its applications
AU - Lin, Gui-Hua
AU - Luo, Mei-Ju
AU - Zhang, Dali
AU - Zhang, Jin
N1 - Funding Information:
The authors are grateful to several anonymous referees and Prof. Xiaojun Chen for their helpful comments and suggestions, which have led to much improvement of the paper. 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.
PY - 2017/9
Y1 - 2017/9
N2 - 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.
AB - 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.
KW - SSOCCP
KW - ERM formulation
KW - Monte Carlo approximation
KW - Natural gas transmission
KW - Optimal power flow
UR - http://www.scopus.com/inward/record.url?scp=85011798156&partnerID=8YFLogxK
U2 - 10.1007/s10107-017-1121-z
DO - 10.1007/s10107-017-1121-z
M3 - Journal article
AN - SCOPUS:85011798156
SN - 0025-5610
VL - 165
SP - 197
EP - 233
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1
ER -