论文标题
基于隐性跟踪的分布式约束耦合优化
Implicit Tracking-Based Distributed Constraint-Coupled Optimization
论文作者
论文摘要
本文研究了一类带有全球耦合平等约束和局部约束集的分布式优化问题。对于缺乏局部约束集的特殊情况，提出和分析了增强的原始偶梯度动力学，但是由于需要使用违反耦合约束的违规，因此无法分布分布。 Benefiting from the brand-new comprehending of a classical distributed unconstrained optimization algorithm, the novel implicit tracking approach is proposed to track the violation distributedly, which leads to the birth of the \underline{i}mplicit tracking-based \underline{d}istribut\underline{e}d \underline{a}ugmented primal-dual gradient dynamics (IDEA).预计的思想变体，即Proj-Idea，进一步设计为处理存在本地约束集的一般情况。借助Lyapunov稳定性理论，分别分析了Idea和Pro-Idea的融合，分别分析了对地图和挖掘物的融合。据我们所知，ProJ-IDEA是第一个恒定的阶梯尺寸分布式算法，它可以解决研究的问题，而无需严格的局部成本功能。此外，如果局部成本功能强烈凸出且平稳，则想法可以实现指数收敛，而耦合约束的情况较弱。最后，进行数值实验以证实我们的理论结果。
A class of distributed optimization problem with a globally coupled equality constraint and local constrained sets is studied in this paper. For its special case where local constrained sets are absent, an augmented primal-dual gradient dynamics is proposed and analyzed, but it cannot be implemented distributedly since the violation of the coupled constraint needs to be used. Benefiting from the brand-new comprehending of a classical distributed unconstrained optimization algorithm, the novel implicit tracking approach is proposed to track the violation distributedly, which leads to the birth of the \underline{i}mplicit tracking-based \underline{d}istribut\underline{e}d \underline{a}ugmented primal-dual gradient dynamics (IDEA). A projected variant of IDEA, i.e., Proj-IDEA, is further designed to deal with the general case where local constrained sets exist. With the aid of the Lyapunov stability theory, the convergences of IDEA and Pro-IDEA over undigraphs and digraphs are analyzed respectively. As far as we know, Proj-IDEA is the first constant step-size distributed algorithm which can solve the studied problem without the need of the strict convexity of local cost functions. Besides, if local cost functions are strongly convex and smooth, IDEA can achieve exponential convergence with a weaker condition about the coupled constraint. Finally, numerical experiments are taken to corroborate our theoretical results.
