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

Switching off the magnetic exchange coupling by quantum resonances

We clarify the role of quantum-well states in magnetic trilayer systems from majority carrier in the ferromagnetic and all carriers in the antiferromagnetic configurations. In addition to numerical and analytic calculations, heuristic pictures are provided to explain effects of a capping layer and side-layer modulation in recent experiments. This immediately offers answers to two unexplained subtle findings in experiments and band-structure calculations, individually. Furthermore, it allows a more flexible tuning of or even turning off the interlayer exchange coupling.Comment: 5 pages, 5 figure