A new convergence analysis and perturbation resilience of some accelerated proximal forwardbackward algorithms with errors

D Reem, A De Pierro - Inverse Problems, 2017 - iopscience.iop.org
… Recently a few works have discussed inexact versions of several accelerated proximal …
inexact versions of a method of Beck and Teboulle (fast iterative shrinkable tresholding algorithm) …

On the acceleration of forward-backward splitting via an inexact Newton method

A Themelis, M Ahookhosh, P Patrinos - Splitting Algorithms, Modern …, 2019 - Springer
We propose a Forward-Backward Truncated-Newton method (FBTN) for minimizing the sum
of two convex functions, one of which smooth. Unlike other proximal Newton methods, our …

Convergence rates of inertial forward-backward algorithms

H Attouch, A Cabot - SIAM Journal on Optimization, 2018 - SIAM
… Thus, we unify most of the existing results based on the accelerated gradient method of …
numbers, we will analyze the convergence properties of the inertial forward-backward algorithm

A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives

M Barré, A Taylor, F Bach - arXiv preprint arXiv:2106.15536, 2021 - arxiv.org
… In this setting, we propose an inexact accelerated forward-backward method for solving (1)
relying on the access to the gradient of f, and to an iterative routine for approximating the …

Convergence of Inexact Forward--Backward Algorithms Using the Forward--Backward Envelope

S Bonettini, M Prato, S Rebegoldi - SIAM Journal on Optimization, 2020 - SIAM
… framework for inexact forward--backward algorithms aimed … Such a framework relies on an
implementable inexactness … metric is allowed into the forward--backward step. The main focus …

The Rate of Convergence of Nesterov's Accelerated Forward-Backward Method is Actually Faster Than

H Attouch, J Peypouquet - SIAM Journal on Optimization, 2016 - SIAM
The forward-backward algorithm is a powerful tool for solving … In the convex setting, a simple
but ingenious acceleration … variant of Nesterov's accelerated forward-backward method, …

Accelerated forward-backward method with fast convergence rate for nonsmooth convex optimization beyond differentiability

W Bian, F Wu - arXiv preprint arXiv:2110.01454, 2021 - arxiv.org
… Abstract We propose an accelerated forward-backwardaccelerated proximal gradient (SAPG)
algorithm. The proposed … term in the SAPG algorithm to get the inexact smoothing ac…

An inertial parallel and asynchronous forwardbackward iteration for distributed convex optimization

G Stathopoulos, CN Jones - Journal of Optimization Theory and …, 2019 - Springer
acceleration techniques with asynchronous implementations of a rather wide family of operator
splitting schemes, this of forwardbackward … our scheme to existing algorithms and how it …

Convergence rate of inertial ForwardBackward algorithm beyond Nesterov's rule

V Apidopoulos, JF Aujol, C Dossal - Mathematical Programming, 2020 - Springer
… 4 we present the same type of analysis for the inexact i-FB algorithm where every new …
(which corresponds to the Nesterov’s accelerated algorithm) seems critical for this non-increasing …

Inertial variable metric techniques for the inexact forward--backward algorithm

S Bonettini, S Rebegoldi, V Ruggiero - SIAM Journal on Scientific Computing, 2018 - SIAM
… This last theoretical result allows one to accelerate the practical convergence … forward-backward
extrapolation method (SFBEM), is shown to outperform the classical FISTA algorithm in …