Ba Khiet Le – Optimization Online

New efficient approach in finding a zero of a maximal monotone operator

Published: 2020/10/05

Convex Optimization, Nonsmooth Optimization fast convergence, maximal monotone operators, proximal point algorithm, regularization

In the paper, we provide a new efficient approach to find a zero of a maximal monotone operator under very mild assumptions. Using a regularization technique and the proximal point algorithm, we can construct a sequence that converges strongly to a solution with at least linear convergence rate. ArticleDownload View PDF

On the linear convergence of the forward-backward splitting algorithm

Published: 2020/09/29

Ba Khiet Le

Convex and Nonsmooth Optimization douglas-rachford algorithm, forward-backward algorithm, linear convergence, maximal monotone operators

In this paper, we establish a linear convergence result for the forward-backward splitting algorithm in the finding a zero of the sum of two maximal monotone operators, where one of them is set-valued strongly monotone and the other is Lipschitz continuous. We show that our convergence rate is better than Douglas–Rachford splitting algorithm’s rate used … Read more