307 research outputs found
Multi-Agent Distributed Optimization via Inexact Consensus ADMM
Multi-agent distributed consensus optimization problems arise in many signal
processing applications. Recently, the alternating direction method of
multipliers (ADMM) has been used for solving this family of problems. ADMM
based distributed optimization method is shown to have faster convergence rate
compared with classic methods based on consensus subgradient, but can be
computationally expensive, especially for problems with complicated structures
or large dimensions. In this paper, we propose low-complexity algorithms that
can reduce the overall computational cost of consensus ADMM by an order of
magnitude for certain large-scale problems. Central to the proposed algorithms
is the use of an inexact step for each ADMM update, which enables the agents to
perform cheap computation at each iteration. Our convergence analyses show that
the proposed methods converge well under some convexity assumptions. Numerical
results show that the proposed algorithms offer considerably lower
computational complexity than the standard ADMM based distributed optimization
methods.Comment: submitted to IEEE Trans. Signal Processing; Revised April 2014 and
August 201
A distributed primal-dual interior-point method for loosely coupled problems using ADMM
In this paper we propose an efficient distributed algorithm for solving
loosely coupled convex optimization problems. The algorithm is based on a
primal-dual interior-point method in which we use the alternating direction
method of multipliers (ADMM) to compute the primal-dual directions at each
iteration of the method. This enables us to join the exceptional convergence
properties of primal-dual interior-point methods with the remarkable
parallelizability of ADMM. The resulting algorithm has superior computational
properties with respect to ADMM directly applied to our problem. The amount of
computations that needs to be conducted by each computing agent is far less. In
particular, the updates for all variables can be expressed in closed form,
irrespective of the type of optimization problem. The most expensive
computational burden of the algorithm occur in the updates of the primal
variables and can be precomputed in each iteration of the interior-point
method. We verify and compare our method to ADMM in numerical experiments.Comment: extended version, 50 pages, 9 figure
Quantized Consensus ADMM for Multi-Agent Distributed Optimization
Multi-agent distributed optimization over a network minimizes a global
objective formed by a sum of local convex functions using only local
computation and communication. We develop and analyze a quantized distributed
algorithm based on the alternating direction method of multipliers (ADMM) when
inter-agent communications are subject to finite capacity and other practical
constraints. While existing quantized ADMM approaches only work for quadratic
local objectives, the proposed algorithm can deal with more general objective
functions (possibly non-smooth) including the LASSO. Under certain convexity
assumptions, our algorithm converges to a consensus within
iterations, where depends on the local
objectives and the network topology, and is a polynomial determined by
the quantization resolution, the distance between initial and optimal variable
values, the local objective functions and the network topology. A tight upper
bound on the consensus error is also obtained which does not depend on the size
of the network.Comment: 30 pages, 4 figures; to be submitted to IEEE Trans. Signal
Processing. arXiv admin note: text overlap with arXiv:1307.5561 by other
author
- …