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Inexact restoration with subsampled trust-region methods 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)

Abstract

Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by randomly sampling components of the sum have received great attention. We propose a new trust-region method which employs suitable approximations of the objective function, gradient and Hessian built via random subsampling techniques. The choice of the sample size is deterministic and ruled by the inexact restoration approach. We discuss local and global properties for finding approximate first- and second-order optimal points and function evaluation complexity results. Numerical experience shows that the new procedure is more efficient, in terms of overall computational cost, than the standard trust-region scheme with subsampled Hessians.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:3:d:10.1007_s10589-020-00196-w
    DOI: 10.1007/s10589-020-00196-w
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    References listed on IDEAS

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    1. Bastin, Fabian & Cirillo, Cinzia & Toint, Philippe L., 2006. "Application of an adaptive Monte Carlo algorithm to mixed logit estimation," Transportation Research Part B: Methodological, Elsevier, vol. 40(7), pages 577-593, August.
    2. Fabian Bastin & Cinzia Cirillo & Philippe Toint, 2006. "An adaptive Monte Carlo algorithm for computing mixed logit estimators," Computational Management Science, Springer, vol. 3(1), pages 55-79, January.
    3. Raghu Pasupathy, 2010. "On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization," Operations Research, INFORMS, vol. 58(4-part-1), pages 889-901, August.
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    Cited by:

    1. 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.
    2. Ernesto G. Birgin, 2020. "Preface of the special issue dedicated to the XII Brazilian workshop on continuous optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 615-619, July.

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