We present a framework for analyzing convergence and local rates of convergence of a
class of descent algorithms, assuming the objective function is weakly convex. The …

This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for
solving convex composite optimization problems over undirected and connected networks …

Many machine learning problems lack strong convexity properties. Fortunately, recent
studies have revealed that first-order algorithms also enjoy linear convergences under …

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a
broad class of nonsmooth composite convex optimization problems without strong convexity …

In this article, we propose a novel dual inexact splitting algorithm (DISA) for distributed
convex composite optimization problems, where the local loss function consists of a smooth …

Many iterative methods in applied mathematics can be thought of as fixed-point iterations,
and such algorithms are usually analyzed analytically, with inequalities. In this paper, we …

Despite the rich literature, the linear convergence of alternating direction method of
multipliers (ADMM) has not been fully understood even for the convex case. For example …

In this paper, we propose a fast stochastic approximation-based subgradient extragradient
algorithm with variance reduction for solving the stochastic variational inequality, where the …

In this paper, we propose a variance-based subgradient extragradient algorithm with line
search for stochastic variational inequality problems by aiming at robustness with respect to …

In this article, we establish the local and global exponential convergence of a primal–dual
dynamics (PDD) for solving equality-constrained optimization problems without strong …