A Unified Distributed Method for Constrained Networked Optimization via Saddle-Point Dynamics
Abstract
This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform these two constrained networked optimization problems into a unified saddle-point problem framework with set constraints. Subsequently, two projection-based primal-dual algorithms via Optimistic Gradient Descent Ascent (OGDA) method and Extra-gradient (EG) method are developed for solving constrained saddle-point problems. It is shown that the developed algorithms achieve exact convergence to a saddle point with an ergodic convergence rate for general convex-concave functions. Based on the proposed primal-dual algorithms via saddle-point dynamics, we develop unified distributed algorithm design and convergence analysis for these two networked optimization problems. Finally, two numerical examples are presented to demonstrate the theoretical results.
Cite
@article{arxiv.2307.07318,
title = {A Unified Distributed Method for Constrained Networked Optimization via Saddle-Point Dynamics},
author = {Yi Huang and Ziyang Meng and Jian Sun and Wei Ren},
journal= {arXiv preprint arXiv:2307.07318},
year = {2023}
}