2021/01/08 by Kui Zhu, Zhu, Kui, Yutao Tang +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC
paper · pdf · doi:10.48550/arxiv.2101.02880
13 pages, 5 figures
openalex publication_date 2021/01/08 · openalex created_date 2021/01/18 · arxiv created 2021/11/20 · arxiv updated 2021/11/23 · openalex updated_date 2026/07/28
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact subgradients of the local objective functions can not be accessed by the agents. To solve this problem, we propose a projected primal-dual dynamics using only the objective function's approximate subgradients. We first prove that the formulated optimization problem can generally be solved with an error depending upon the accuracy of the available subgradients. Then, we show the exact solvability of this distributed optimization problem when the accumulated approximation error of inexact subgradients is not too large. After that, we also give a novel componentwise normalized variant to improve the transient behavior of the convergent sequence. The effectiveness of our algorithms is verified by a numerical example.