Author

Naoki Marumo

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Preprint Jul 2026

Parameter-Free Cubic-Regularized Newton Method: Sharp Complexity and Generalized Smoothness

A variant of the cubic-regularized Newton method for nonconvex optimization that is parameter-free in that it requires no prior knowledge of problem-dependent parameters is analyzed, and an oracle complexity bound is derived for finding an $(varepsilon, \delta)-second-order stationary point.

Shaoying Fang, Naoki Marumo, Akiko Takeda · 1 citation