A geometric alternative to Nesterov's accelerated gradient descent
This work addresses optimization efficiency for machine learning and numerical computing, but it appears incremental as it builds on existing accelerated gradient methods.
The authors tackled the problem of unconstrained optimization for smooth, strongly convex functions by proposing a new method that achieves the same optimal convergence rate as Nesterov's accelerated gradient descent, with numerical evidence suggesting it can be superior in some cases.
We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric interpretation, loosely inspired by the ellipsoid method. We provide some numerical evidence that the new method can be superior to Nesterov's accelerated gradient descent.