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

• URL: http://arxiv.org/abs/2109.11502v1
• Date: Thu, 23 Sep 2021 17:12:17 GMT
• Title: Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming
• Authors: Sen Na, Mihai Anitescu, Mladen Kolar
• Abstract summary: We study nonlinear optimization problems with objective and deterministic equality and inequality constraints. We propose an active-set sequentialAdaptive programming algorithm, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the parameters of augmented Lagrangian and performs line search to decide the stepsize.
• Score: 17.9230793188835
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We study nonlinear optimization problems with 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, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of 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 prior work \cite{Na2021Adaptive} by allowing nonlinear inequality constraints. We demonstrate the performance of the algorithm on a subset of nonlinear problems collected in the CUTEst test set.

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