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

Author

Listed:
  • Albert S. Berahas

    (University of Michigan)

  • Jiahao Shi

    (University of Michigan)

  • Zihong Yi

    (University of Michigan)

  • Baoyu Zhou

    (University of Chicago)

Abstract

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.

Suggested Citation

  • Albert S. Berahas & Jiahao Shi & Zihong Yi & Baoyu Zhou, 2023. "Accelerating stochastic sequential quadratic programming for equality constrained optimization using predictive variance reduction," Computational Optimization and Applications, Springer, vol. 86(1), pages 79-116, September.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00483-2
    DOI: 10.1007/s10589-023-00483-2
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    References listed on IDEAS

    as
    1. Nilanjan Chatterjee & Yi-Hau Chen & Paige Maas & Raymond J. Carroll, 2016. "Constrained Maximum Likelihood Estimation for Model Calibration Using Summary-Level Information From External Big Data Sources," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 107-117, March.
    2. Jianchao Bai & William W. Hager & Hongchao Zhang, 2022. "An inexact accelerated stochastic ADMM for separable convex optimization," Computational Optimization and Applications, Springer, vol. 81(2), pages 479-518, March.
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