Starting from where a first course in convex optimization leaves off, this text presents a
unified analysis of first-order optimization methods–including parallel-distributed algorithms …

Operator-splitting methods convert optimization and inclusion problems into fixed-point
equations; when applied to convex optimization and monotone inclusion problems, the …

Recently, several convergence rate results for Douglas-Rachford splitting and the
alternating direction method of multipliers (ADMM) have been presented in the literature. In …

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 …

Abstract The Alternating Direction Method of Multipliers (ADMM) is widely used for linearly
constrained convex problems. It is proven to have an o (1/K) o (1/K) nonergodic …

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

Recently, several authors have shown local and global convergence rate results for Douglas–
Rachford splitting under strong monotonicity, Lipschitz continuity, and cocoercivity …

We introduce regularity notions for averaged nonexpansive operators. Combined with
regularity notions of their fixed point sets, we obtain linear and strong convergence results …

In this paper, we investigate the Douglas–Rachford method (DR) for two closed (possibly
nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the …

Although the central role of educational intermediaries that can connect research and
practice is increasingly appreciated, our present understanding of their motivations …