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A stochastic first-order trust-region method with inexact restoration for finite-sum minimization

Author

Listed:
  • Stefania Bellavia

    (Università degli Studi di Firenze)

  • Nataša Krejić

    (University of Novi Sad)

  • Benedetta Morini

    (Università degli Studi di Firenze)

  • Simone Rebegoldi

    (Università degli Studi di Firenze)

Abstract

We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved.

Suggested Citation

  • Stefania Bellavia & Nataša Krejić & Benedetta Morini & Simone Rebegoldi, 2023. "A stochastic first-order trust-region method with inexact restoration for finite-sum minimization," Computational Optimization and Applications, Springer, vol. 84(1), pages 53-84, January.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:1:d:10.1007_s10589-022-00430-7
    DOI: 10.1007/s10589-022-00430-7
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    References listed on IDEAS

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    1. Stefania Bellavia & Nataša Krejić & Benedetta Morini, 2020. "Inexact restoration with subsampled trust-region methods for finite-sum minimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 701-736, July.
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