2 citations · 2 across the 8 of their papers we have counts for
8 papers
A restart-free accelerated algorithm for nonconvex minimization: continuous- and discrete-time analysis
Kansei Ushiyama, Shun Sato
We propose two deterministic momentum-based first-order methods for minimizing lower-bounded nonconvex functions with Lipschitz-continuous gradients and Hessians. Both methods atta…
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…
Mathematical analysis and numerical comparison of energy-conservative schemes for the Zakharov equations
Shuto Kawai, Shun Sato, Takayasu Matsuo
Furihata and Matsuo proposed in 2010 an energy-conserving scheme for the Zakharov equations, as an application of the discrete variational derivative method (DVDM). This scheme is…
A self-adaptive moving mesh method for the short pulse equation via its hodograph link to the sine-Gordon equation
S. Sato, K. Oguma, T. Matsuo +1
The short pulse equation was introduced by Schaefer--Wayne (2004) for modeling the propagation of ultrashort optical pulses. While it can describe a wide range of solutions, its ul…