On the Q-linear convergence of Distributed Generalized ADMM under non-strongly convex function components

Autor:	Maros, Marie, Jaldén, Joakim
Rok vydání:	2018
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	Solving optimization problems in multi-agent networks where each agent only has partial knowledge of the problem has become an increasingly important problem. In this paper we consider the problem of minimizing the sum of $n$ convex functions. We assume that each function is only known by one agent. We show that Generalized Distributed ADMM converges Q-linearly to the solution of the mentioned optimization problem if the over all objective function is strongly convex but the functions known by each agent are allowed to be only convex. Establishing Q-linear convergence allows for tracking statements that can not be made if only R-linear convergence is guaranteed. Further, we establish the equivalence between Generalized Distributed ADMM and P-EXTRA for a sub-set of mixing matrices. This equivalence yields insights in the convergence of P-EXTRA when overshooting to accelerate convergence. Comment: Submitted to IEEE Transactions on Signal and Information Processing over Networks
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.01660 Zobrazit plný text záznamu View this record from Arxiv