Volume 28, 2022
|Number of page(s)||34|
|Published online||02 June 2022|
A primal-dual flow for affine constrained convex optimization
School of Mathematical Sciences, Peking University, Beijing 100871, China
* Corresponding author: email@example.com
Accepted: 20 April 2022
We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our flow model is proved to possess the exponential decay property, in terms of a tailored Lyapunov function. Then two primal-dual methods are obtained from numerical discretizations of the continuous problem, and global nonergodic linear convergence rate is established via a discrete Lyapunov function. Instead of solving the subproblem of the primal variable, we apply the semi-smooth Newton iteration to the inner problem with respect to the multiplier, provided that there are some additional properties such as semi-smoothness and sparsity. Finally, numerical tests on the linearly constrained l1-l2 minimization and the tot al-variation based image denoising model have been provided.
Mathematics Subject Classification: 37M99 / 37N40 / 65K05 / 90C25
Key words: Convex optimization / linear constraint / dynamical system / Lyapunov function / exponential decay / discretization / nonergodic linear rate / primal-dual algorithm / semi-smooth Newton method / l1-l2 minimization / total-variation model
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.