This paper describes an accelerated HPE-type method based on general Bregman distances for solving monotone saddle-point (SP) problems. The algorithm is a special instance of a non-Euclidean hybrid proximal extragradient framework introduced by Svaiter and Solodov [28] where the prox sub-inclusions are solved using an accelerated gradient method. It generalizes the accelerated HPE algorithm presented … Read more

An O(1/k) Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm

An earlier paper proved the convergence of a variable stepsize Bregman operator splitting algorithm (BOSVS) for minimizing $\phi(Bu)+H(u)$ where $H$ and $\phi$ are convex functions, and $\phi$ is possibly nonsmooth. The algorithm was shown to be relatively efficient when applied to partially parallel magnetic resonance image reconstruction problems. In this paper, the convergence rate of … Read more

On the ergodic convergence rates of a first-order primal-dual algorithm

We revisit the proofs of convergence for a first order primal-dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a more general version, with simpler proofs and more complete results. Article Download View On the ergodic convergence rates of a first-order primal-dual algorithm

An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and its Implications to Second-Order Methods

This paper presents an accelerated variant of the hybrid proximal extragradient (HPE) method for convex optimization, referred to as the accelerated HPE (A-HPE) method. Iteration-complexity results are established for the A-HPE method, as well as a special version of it, where a large stepsize condition is imposed. Two specific implementations of the A-HPE method are … Read more