Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Non-smooth Approach
Optimization and Control
2020-01-06 v2
Abstract
We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact penalty method, we reformulate the problem equivalently as a standard distributed one without consensus constraints. Then we design a distributed projected subgradient algorithm with the help of differential inclusions. Furthermore, we show that the algorithm converges to the optimal solution exponentially for strongly convex objective functions.
Cite
@article{arxiv.2001.00509,
title = {Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Non-smooth Approach},
author = {Weijian Li and Xianlin Zeng and Shu Liang and Yiguang Hong},
journal= {arXiv preprint arXiv:2001.00509},
year = {2020}
}