Work

Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms

Year: 2014

Type: article

Abstract: We study distributed optimization where nodes cooperatively minimize the sum of their individual, locally known, convex costs fi(x)'s; x ϵ ℝdis global. Distributed augmented Lagrangian (AL) methods have good empirical performance on several signal processing and learning applications, but there is limited understanding of their convergence rates and how it depends on the underlying network. This paper establishes globally linear (geometric) convergence rates of a class of deterministic and randomized distributed AL methods, when the fi's are twice continuously differentiable and have a bounded Hessian. We give explicit dependence of the convergence rates on the underlying network parameters. Simulations illustrate our analytical findings.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2014.2363299

Authors: Dusan Jakovetic, Jose M. F. Moura, Joao Xavier

Institutions: University of Lisbon, University of Novi Sad, Carnegie Mellon University, Instituto Superior Técnico

Language: English

Topic: Distributed Control Multi-Agent Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Fundação para a Ciência e a Tecnologia, Air Force Office of Scientific Research

Awards: Novas metodologias de processamento de informação para redes inteligentes de sensores, G3318123485, Engenharia Electrotécnica e de Computadores, Optimização Distribuída e Controlo de Sistemas de Distribuição de Água de Larga Escala, G8952488736