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Optimal step length for the maximal decrease of a self-concordant function by the Newton method

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Abstract

In this paper we consider the problem of finding the optimal step length for the Newton method on the class of self-concordant functions, with the decrease in function value as criterion. We formulate this problem as an optimal control problem and use optimal control theory to solve it.

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Authors and Affiliations

  1. LJK, University Grenoble Alpes, 38000, Grenoble, France

    Anastasia Ivanova

  2. HSE University, Moscow, Russian Federation

    Anastasia Ivanova

  3. CNRS, Grenoble INP, LJK, University Grenoble Alpes, 38000, Grenoble, France

    Roland Hildebrand

  4. MMO Laboratory, MIPT, 117303, Moscow, Russia

    Roland Hildebrand

Authors
  1. Anastasia Ivanova
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  2. Roland Hildebrand
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Correspondence to Anastasia Ivanova.

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Ivanova, A., Hildebrand, R. Optimal step length for the maximal decrease of a self-concordant function by the Newton method. Optim Lett 18, 847–854 (2024). https://doi.org/10.1007/s11590-023-02035-3

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  • DOI: https://doi.org/10.1007/s11590-023-02035-3

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