论文标题
NPGA：用于分散约束耦合优化的统一算法框架
NPGA: A Unified Algorithmic Framework for Decentralized Constraint-Coupled Optimization
论文作者
论文摘要
这项工作着重于一类普遍分散的约束耦合优化问题。我们提出了一种新型的嵌套原始双侧梯度算法（NPGA），该算法可以在最弱的已知条件下实现线性收敛，其理论收敛速率超过了所有已知结果。更重要的是，NPGA不仅可以用作算法，而且用作统一的算法框架，涵盖了各种现有算法作为特殊情况。通过设计不同的网络矩阵，我们可以通过方便地利用NPGA的收敛结果来得出多种NPGA版本，并分析其收敛性，从而实现了更有效的算法的设计。最后，我们进行数值实验，以比较NPGA和现有算法的收敛速率，从而为NPGA的出色性能提供了经验证据。
This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its theoretical convergence rate surpasses all known results. More importantly, NPGA serves not only as an algorithm but also as a unified algorithmic framework, encompassing various existing algorithms as special cases. By designing different network matrices, we can derive numerous versions of NPGA and analyze their convergences by leveraging the convergence results of NPGA conveniently, thereby enabling the design of more efficient algorithms. Finally, we conduct numerical experiments to compare the convergence rates of NPGA and existing algorithms, providing empirical evidence for the superior performance of NPGA.
