In this paper, we analyze the convergence of the alternating direction method of multipliers
(ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, ϕ (x_0 …

We introduce a first-order method for solving very large convex cone programs. The method
uses an operator splitting method, the alternating directions method of multipliers, to solve …

The formulation _ x, y~ f (x)+ g (y),\quad subject to Ax+ By= b, min x, yf (x)+ g (y), subject to A
x+ B y= b, where f and g are extended-value convex functions, arises in many application …

Finding a fixed point to a nonexpansive operator, ie, x^*=Tx^*, abstracts many problems in
numerical linear algebra, optimization, and other areas of data science. To solve fixed-point …

Operator-splitting schemes are iterative algorithms for solving many types of numerical
problems. A lot is known about these methods: they converge, and in many cases we know …

Convex nonsmooth optimization problems, whose solutions live in very high dimensional
spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as …

Although originally designed and analyzed for convex problems, the alternating direction
method of multipliers (ADMM) and its close relatives, Douglas--Rachford splitting (DRS) and …

Federated learning is a framework for distributed optimization that places emphasis on
communication efficiency. In particular, it follows a client-server broadcast model and is …

In this paper, we provide a comprehensive convergence rate analysis of the Douglas-
Rachford splitting (DRS), Peaceman-Rachford splitting (PRS), and alternating direction …

In this paper, we propose a new primal–dual algorithm for minimizing f (x)+ g (x)+ h (A x) f
(x)+ g (x)+ h (A x), where f, g, and h are proper lower semi-continuous convex functions, f is …