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Globalized inexact proximal Newton-type methods for nonconvex composite functions

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  • Christian Kanzow

    (University of Würzburg, Institute of Mathematics)

  • Theresa Lechner

    (University of Würzburg, Institute of Mathematics)

Abstract

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. The current literature on these classes of methods almost exclusively considers the case where also the smooth term is convex. Here we present a globalized proximal Newton-type method which allows the smooth term to be nonconvex. The method is shown to have nice global and local convergence properties, and some numerical results indicate that this method is very promising also from a practical point of view.

Suggested Citation

  • Christian Kanzow & Theresa Lechner, 2021. "Globalized inexact proximal Newton-type methods for nonconvex composite functions," Computational Optimization and Applications, Springer, vol. 78(2), pages 377-410, March.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:2:d:10.1007_s10589-020-00243-6
    DOI: 10.1007/s10589-020-00243-6
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    References listed on IDEAS

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    Cited by:

    1. Simeon vom Dahl & Christian Kanzow, 2024. "An inexact regularized proximal Newton method without line search," Computational Optimization and Applications, Springer, vol. 89(3), pages 585-624, December.
    2. Christian Kanzow & Theresa Lechner, 2022. "COAP 2021 Best Paper Prize," Computational Optimization and Applications, Springer, vol. 83(3), pages 723-726, December.

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