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: firstname.lastname@example.org
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
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