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math.OC2026
Parameter-Free Cubic-Regularized Newton Method: Sharp Complexity and Generalized Smoothness
Shaoying Fang, Naoki Marumo, Akiko Takeda
We analyze a variant of the cubic-regularized Newton method for nonconvex optimization. This variant is parameter-free in that it requires no prior knowledge of problem-dependent p…
math.OC2026
A General Recipe for Parameter-Free Nonconvex Optimization via Higher-Order Regularization
Naoki Marumo, Akiko Takeda
We develop a systematic framework for constructing parameter-free algorithms for smooth nonconvex optimization. The framework is based on higher-order regularization: each step is…
math.OC2026
Practical Regularized Quasi-Newton Methods with Inexact Function Values
Hiroki Hamaguchi, Naoki Marumo, Akiko Takeda
Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods co…