4 papers
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 new unified framework for designing convex optimization methods with prescribed theoretical convergence estimates: A numerical analysis approach
Kansei Ushiyama, Shun Sato, Takayasu Matsuo
We propose a new unified framework for describing and designing gradient-based convex optimization methods from a numerical analysis perspective. There the key is the new concept o…
Essential convergence rate of ordinary differential equations appearing in optimization
Kansei Ushiyama, Shun Sato, Takayasu Matsuo
Some continuous optimization methods can be connected to ordinary differential equations (ODEs) by taking continuous limits, and their convergence rates can be explained by the ODE…