TY - JOUR
T1 - Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems
AU - Wang, Guoxin
AU - Zhang, Jin
AU - Zeng, Bo
AU - Lin, Gui Hua
N1 - Funding Information:
This work was supported in part by NSFC (Nos. 11431004, U1504105, 11671250, 11601458, 11771255), Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034), and HKBU grants (Nos. FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J).
PY - 2018/3/1
Y1 - 2018/3/1
N2 - This paper considers a class of stochastic linear second-order cone complementarity problems (SLSOCCP). Noticing that the SLSOCCP does not have a solution suitable to all realizations in general, we present a deterministic formulation, called the expected residual minimization (ERM) formulation, for it. The coercive property of the ERM problem and the robustness of its solutions are discussed. Due to the existence of expectation in the ERM problem, we employ the Monte Carlo approximation techniques to approximate the ERM problem and show that, under mild conditions, this approximation approach possesses exponential convergence rate. Then, we extend the above results to a general mixed SLSOCCP. Furthermore, we apply the theoretical results to a stochastic optimal power flow model in radial network and report some numerical dispatching experiments for real-world Southern California Edison 47-bus network.
AB - This paper considers a class of stochastic linear second-order cone complementarity problems (SLSOCCP). Noticing that the SLSOCCP does not have a solution suitable to all realizations in general, we present a deterministic formulation, called the expected residual minimization (ERM) formulation, for it. The coercive property of the ERM problem and the robustness of its solutions are discussed. Due to the existence of expectation in the ERM problem, we employ the Monte Carlo approximation techniques to approximate the ERM problem and show that, under mild conditions, this approximation approach possesses exponential convergence rate. Then, we extend the above results to a general mixed SLSOCCP. Furthermore, we apply the theoretical results to a stochastic optimal power flow model in radial network and report some numerical dispatching experiments for real-world Southern California Edison 47-bus network.
KW - ERM formulation
KW - Monte Carlo approximation
KW - Nonlinear programming
KW - Radial network
KW - SLSOCCP
UR - http://www.scopus.com/inward/record.url?scp=85030261303&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2017.09.008
DO - 10.1016/j.ejor.2017.09.008
M3 - Journal article
AN - SCOPUS:85030261303
SN - 0377-2217
VL - 265
SP - 437
EP - 447
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -