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

We introduce a class of first-order methods for smooth constrained optimization that are
based on an analogy to non-smooth dynamical systems. Two distinctive features of our …

Traditionally, numerical algorithms are seen as isolated pieces of code confined to an in
silico existence. However, this perspective is inappropriate for many modern computational …

We consider a distributed learning problem, where agents minimize a global objective
function by exchanging information over a network. Our approach has two distinct …

We exploit analogies between first-order algorithms for constrained optimization and non-
smooth dynamical systems to design a new class of accelerated first-order algorithms for …

In a recent paper, Muehlebach and Jordan (2021a) proposed a novel algorithm for
constrained optimization that uses original ideals from nonsmooth dynamical systems. In this …

We study the exponential stability of continuous-time primal-dual gradient flow dynamics for
convex optimization problems with linear equality constraints. Without making any …

We study performance of momentum-based accelerated first-order optimization algorithms
in the presence of additive white stochastic disturbances. For strongly convex quadratic …

We investigate how adaptive step size methods from numerical analysis can be used to
speed up optimization routines. In contrast to line search strategies, the proposed methods …

Deep learning technologies are skyrocketing in popularity across a wide range of domains,
with groundbreaking accomplishments in fields such as natural language processing …