Accelerating stochastic sequential quadratic programming for equality constrained optimization using predictive variance reduction

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that employs variance reduction in the gradient approximations. U...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 86; no. 1; pp. 79 - 116
Main Authors: Berahas, Albert S., Shi, Jiahao, Yi, Zihong, Zhou, Baoyu
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2023
Springer Nature B.V
Subjects:
Algorithms
Approximation
Convex and Discrete Geometry
Machine learning
Management Science
Mathematics
Mathematics and Statistics
Methods
Neighborhoods
Operations Research
Operations Research/Decision Theory
Optimization
Quadratic programming
Reduction
Statistics
Sequential quadratic programming (SQP)
Equality constraints
Constrained stochastic optimization
Variance reduction
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that employs variance reduction in the gradient approximations. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our proposed algorithm converges to zero in expectation from arbitrary starting points, for both constant and adaptive step size strategies. Finally, we demonstrate the practical performance of our proposed algorithm on constrained binary classification problems that arise in machine learning.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-023-00483-2