An inexact semismooth Newton SAA-based algorithm for stochastic nonsmooth SOC complementarity problems with application to a stochastic power flow programming problem

In this paper, we study a stochastic nonsmooth second-order cone complementarity problem (SNS-SOCCP), in which the mathematical expectations are involved and the function is locally Lipschitz continuous but not necessarily continuously differentiable everywhere. By using some second-order cone complementarity function, SNS-SOCCP is reformulated equivalently into a system of stochastic nonsmooth equations. Based on this reformulation, we derive an explicit generalized Jacobian involved. Then, we design an inexact semismooth Newton algorithm based on an SAA (sample average approximation) technique to solve the stochastic nonsmooth equations. We investigate the convergence properties of the proposed algorithm under suitable conditions. Finally, to prove the effectiveness of the proposed algorithm, we solve numerically a stochastic power flow programming problem.