Motivated by recent increased interest in optimization algorithms for non-convex
optimization in application to training deep neural networks and other optimization problems …

We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …

We consider distributed convex-concave saddle point problems over arbitrary connected
undirected networks and propose a decentralized distributed algorithm for their solution. The …

In the last few years, the theory of decentralized distributed convex optimization has made
significant progress. The lower bounds on communications rounds and oracle calls have …

In this article, we propose a novel solution for nonconvex problems of multiple variables,
especially for those typically solved by an alternating minimization (AM) strategy that splits …

This paper discusses the efficiency of Hybrid Primal-Dual (HPD) type algorithms to
approximately solve discrete Optimal Transport (OT) and Wasserstein Barycenter (WB) …

Optimal transport is an important tool in machine learning, allowing to capture geometric
properties of the data through a linear program on transport polytopes. We present a single …

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal
transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical …

By choosing a suitable function space as the dual to the non-negative measure cone, we
study in a unified framework a class of functional saddle-point optimization problems, which …

We present several new complexity results for the entropic regularized algorithms that
approximately solve the optimal transport (OT) problem between two discrete probability …