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Inertial Newton Algorithms Avoiding Strict Saddle Points

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  • Camille Castera

    (CNRS - IRIT, Université de Toulouse)

Abstract

We study the asymptotic behavior of second-order algorithms mixing Newton’s method and inertial gradient descent in non-convex landscapes. We show that, despite the Newtonian behavior of these methods, they almost always escape strict saddle points. We also evidence the role played by the hyper-parameters of these methods in their qualitative behavior near critical points. The theoretical results are supported by numerical illustrations.

Suggested Citation

  • Camille Castera, 2023. "Inertial Newton Algorithms Avoiding Strict Saddle Points," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 881-903, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02330-0
    DOI: 10.1007/s10957-023-02330-0
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    References listed on IDEAS

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    1. Peter Ochs, 2018. "Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 153-180, April.
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