4 papers · 1 filter
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…
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…
A -accelerated FISTA for composite strongly convex problems
Kansei Ushiyama
In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing composite convex functions expressed as the sum of a smooth function and a possibl…
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…