Distributed online optimization and online games have been increasingly researched in the
last decade, mostly motivated by their wide applications in sensor networks, robotics (eg …

In a real Hilbert space H, in order to develop fast optimization methods, we analyze the
asymptotic behavior, as time t tends to infinity, of a large class of autonomous dissipative …

We analyze feature learning in infinite-width neural networks trained with gradient flow
through a self-consistent dynamical field theory. We construct a collection of deterministic …

Accelerated optimization methods, such as Nesterov's accelerated gradient method, play a
significant role in optimization. Several accelerated methods are provably optimal under …

In this study, a framework for processing gradient algorithms is proposed in accordance with
nabla fractional-order system theory. Unlike most of the literature, the gradient algorithm is …

Although Nesterov's accelerated gradient method (AGM) has been studied from various
perspectives, it remains unclear why the most popular forms of AGMs must handle convex …

We analyze continuous-time models of accelerated gradient methods through deriving
conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics …

In this manuscript we study the properties of a family of a second-order differential equations
with damping, its discretizations, and their connections with accelerated optimization …

Arguably, the two most popular accelerated or momentum-based optimization methods are
Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different …

In this paper we study two-player bilinear zero-sum games with constrained strategy spaces.
An instance of natural occurrences of such constraints is when mixed strategies are used …