6 papers
A Restart-Free Accelerated Algorithm for Non-Convex Minimization: Continuous and Discrete Analysis
Kansei Ushiyama, Shun Sato
We propose two novel first-order methods for minimizing nonconvex functions with Lipschitz-continuous gradients and Hessians. These algorithms attain an -approximate f…
Structural Inconsistency and Stability Classification of Multi-symplectic Diamond Schemes
Kaito Sato, Shun Sato, Takayasu Matsuo
Multi-symplectic diamond schemes proposed by McLachlan and Wilkins (2015) provide a framework for the numerical integration of Hamiltonian partial differential equations, combining…
A Mathematical Analysis of a Smooth-Convex-Concave Splitting Scheme for the Swift--Hohenberg Equation
Yuki Yonekura, Daiki Iwade, Shun Sato +1
The Swift--Hohenberg equation is a widely studied fourth-order model, originally proposed to describe hydrodynamic fluctuations. It admits an energy-dissipation law and, under suit…
Essential Convergence Rates of Continuous-Time Models for Optimization Methods
Kansei Ushiyama, Shun Sato, Takayasu Matsuo
Designing and analyzing optimization methods via continuous-time models expressed as ordinary differential equations (ODEs) is a promising approach for its intuitiveness and simpli…
Analysis of nonquadratic energy-conservative schemes for KdV type-equations
Shuto Kawai, Shun Sato, Takayasu Matsuo
Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes…
A novel interpretation of Nesterov's acceleration via variable step-size linear multistep methods
Ryota Nozawa, Shun Sato, Takayasu Matsuo
Nesterov's acceleration in continuous optimization can be understood in a novel way when Nesterov's accelerated gradient (NAG) method is considered as a linear multistep (LM) metho…