Author

Shota Takahashi

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Preprint Sep 2026

Linesearch-Free Nonlinearly Preconditioned GD with Semiautomatic Geometry Design

Nonlinear preconditioning makes it possible to adapt gradient updates to the growth of the objective's curvature, but combining its design with suitable stepsize selection is challenging. We propose adaptive dual preconditioned gradient descent (adaptive DPGD), which combines curvature-based preconditioner design with...

Daiki Iwade, Shota Takahashi, Akiko Takeda · 0 citations

Preprint Sep 2026

Beyond Polytopes: Damped Newton Frank--Wolfe Methods over Compact Convex Sets

We study convex optimization over compact convex sets for twice differentiable objective functions with positive definite Hessians, assuming access to the feasible set through a linear minimization oracle. Existing second-order Frank--Wolfe methods either provide only a local linear rate over general convex sets or ach...

Shota Takahashi, Akiko Takeda · 0 citations

Preprint Sep 2026

Accelerated Bregman Proximal Gradient Methods from Dual Geometric Perspectives

We study Bregman proximal gradient (BPG) algorithms under relative smoothness for convex, relatively strongly convex, and nonconvex objectives. Existing accelerated BPG algorithms for convex objectives typically require additional assumptions on Bregman divergences, most notably triangle-scaling conditions, which can l...

Yuya Yamashita, Shota Takahashi, Akiko Takeda · 0 citations