Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming

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Abstract
We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. We propose an active-set stochastic sequential quadratic programming algorithm that uses a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of the augmented Lagrangian, and performs stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the "liminf" of the KKT residuals converges to zero almost surely. Our algorithm and analysis further develop the work of Na et al. (2021) by allowing nonlinear inequality constraints without requiring the strict complementary condition. We demonstrate the performance of the algorithm on a subset of nonlinear problems collected in CUTEst test set.

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