On the convergence of the forward-backward splitting method with linesearches
Optimization and Control
2016-10-17 v4
Abstract
In this paper we focus on the convergence analysis of the forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces when the objective function is the sum of two convex functions. Assuming that one of the functions is Fr\'echet differentiable and using two new linesearches, the weak convergence is established without any Lipschitz continuity assumption on the gradient. Furthermore, we obtain many complexity results of cost values at the iterates when the stepsizes are bounded below by a positive constant.
Keywords
Cite
@article{arxiv.1501.02501,
title = {On the convergence of the forward-backward splitting method with linesearches},
author = {J. Y. Bello Cruz and T. T. A. Nghia},
journal= {arXiv preprint arXiv:1501.02501},
year = {2016}
}