Inequality constrained stochastic nonlinear optimization via active-set sequential quadratic programming

Abstract We study nonlinear optimization problems with a stochastic objective and deterministic equality inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. propose an active-set sequential quadratic programming (StoSQP) algorithm that utilizes differentiable exact augmented Lagrangian as the merit function. The adaptively selects penalty parameters of Lagrangian, performs line search to decide stepsize. global convergence is established: for any initialization, KKT residuals converge zero almost surely . Our analysis further develop prior work Na et al. (Math Program, 2022. https://doi.org/10.1007/s10107-022-01846-z ). Specifically, we allow constraints without requiring strict complementary condition; refine some designs (2022) such feasibility error condition monotonically increasing sample size; strengthen guarantee; improve complexity on Hessian. demonstrate performance designed subset collected CUTEst test set constrained logistic regression problems.