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

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 quadra...

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Veröffentlicht in:Mathematical programming Jg. 202; H. 1-2; S. 279 - 353
Hauptverfasser: Na, Sen, Anitescu, Mihai, Kolar, Mladen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Springer
Schlagworte:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Neural networks
Numerical Analysis
Theoretical
90C30
Sequential quadratic programming
90C55
Exact augmented Lagrangian
90-08
90C90
90C15
90C26
Inequality constraints
Stochastic optimization
ISSN:0025-5610, 1436-4646
Online-Zugang:Volltext
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Zusammenfassung: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 (StoSQP) algorithm that utilizes a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of the augmented Lagrangian, and performs a stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the KKT residuals converge to zero almost surely . Our algorithm and analysis further develop the prior work of Na et al. (Math Program, 2022. https://doi.org/10.1007/s10107-022-01846-z ). Specifically, we allow nonlinear inequality constraints without requiring the strict complementary condition; refine some of designs in Na et al. (2022) such as the feasibility error condition and the monotonically increasing sample size; strengthen the global convergence guarantee; and improve the sample complexity on the objective Hessian. We demonstrate the performance of the designed algorithm on a subset of nonlinear problems collected in CUTEst test set and on constrained logistic regression problems.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-023-01935-7