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

Asynchronous Distributed ADMM for Large-Scale Optimization- Part I: Algorithm and Convergence Analysis

Aiming at solving large-scale learning problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the learning problem as a consensus problem, the ADMM can be used to solve the consensus problem in a fully parallel fashion over a computer network with a star topology. However, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by the slowest workers. This is particularly true in a heterogeneous network where the computing nodes experience different computation and communication delays. In this paper, we propose an asynchronous distributed ADMM (AD-AMM) which can effectively improve the time efficiency of distributed optimization. Our main interest lies in analyzing the convergence conditions of the AD-ADMM, under the popular partially asynchronous model, which is defined based on a maximum tolerable delay of the network. Specifically, by considering general and possibly non-convex cost functions, we show that the AD-ADMM is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points as long as the algorithm parameters are chosen appropriately according to the network delay. We further illustrate that the asynchrony of the ADMM has to be handled with care, as slightly modifying the implementation of the AD-ADMM can jeopardize the algorithm convergence, even under a standard convex setting.Comment: 37 page

Semileptonic Decays of BcB_c Meson to a P-Wave Charmonium State χc\chi_c or hch_c

The semileptonic decays of meson $B_c$ to a P-wave charmonium state $\chi_c(^3P_J)$ or $h_c(^1P_1)$ are computed. The results show that the decays are sizable so they are accessible in Tevatron and in LHC, especially, with the detectors LHCB and BTeV in the foreseeable future, and of them, the one to the $^1P_1$ charmonium state potentially offers us a novel window to see the unconfirmed $h_c$ particle. In addition, it is pointed out that since the two charmonium radiative decays $\chi_c(^3P_{1,2}) \to J/\psi+\gamma$ have sizable branching ratios, the cascade decays of the concerned decays and the charmonium radiative decays may affect the result of the observing the $B_c$ meson through the semileptonic decays $B_{c}\to {J/\psi}+{l}+\nu_{l}$ substantially.Comment: 8 pages, 2 figure