Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems

Guoxin Wang, Jin Zhang, Bo Zeng and Gui-Hua Lin

European Journal of Operational Research, 2018, vol. 265, issue 2, 437-447

Abstract: 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.

Keywords: Nonlinear programming; SLSOCCP; ERM formulation; Monte Carlo approximation; Radial network (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:265:y:2018:i:2:p:437-447

DOI: 10.1016/j.ejor.2017.09.008

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