Inertial Newton Algorithms Avoiding Strict Saddle Points

Camille Castera ()
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Camille Castera: CNRS - IRIT, Université de Toulouse

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 3, No 2, 903 pages

Abstract: 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.

Keywords: Non-convex optimization; Algorithms for machine learning; Dynamical systems; Convergence analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02330-0

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