Year: 2019
Type: preprint
Abstract: This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is $O(\tfrac{1}{t^2})$ by choosing suitable parameters. As far as we know, this is the first continuous-time primal-dual accelerated method that can obtain the optimal rate. Then this work applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.
Source: arXiv (Cornell University)
Authors: Zeng, Xianlin, Lei, Jinlong, Chen, Jie
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4366604739