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arXiv · 2111.04596

Inertial Newton Algorithms Avoiding Strict Saddle Points

Camille Castera
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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.

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Camille Castera. 2021-11-08. Inertial Newton Algorithms Avoiding Strict Saddle Points. https://doi.org/10.1007/s10957-023-02330-0

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