Optimization is a ubiquitous modeling tool and is often deployed in settings which
repeatedly solve similar instances of the same problem. Amortized optimization methods …

We propose computationally tractable accelerated first-order methods for Riemannian
optimization, extending the Nesterov accelerated gradient (NAG) method. For both …

It was shown recently by W. Su, S. Boyd, and E. Candes, J. Mach. Learn. Res., 17 (2016),
pp. 1--43 that Nesterov's accelerated gradient method for minimizing a smooth convex …

A variational formulation for accelerated optimization on normed vector spaces was recently
introduced in Wibisono et al.(PNAS 113: E7351–E7358, 2016), and later generalized to the …

It is well known that symplectic integrators lose their near energy preservation properties
when variable time-steps are used. The most common approach to combining adaptive time …

A variational framework for accelerated optimization was recently introduced on normed
vector spaces and Riemannian manifolds in Wibisono et al.(2016) and Duruisseaux and …

In this paper, we generalize the Nesterov accelerated gradient (NAG) method to solve
Riemannian optimization problems in a computationally tractable manner. The iteration …

We consider the fundamental task of optimizing a real-valued function defined in a
potentially high-dimensional Euclidean space, such as the loss function in many machine …