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

Collider search of light dark matter model with dark sector decay

We explore the possibility that the dark matter relic density is not produced by thermal mechanism directly, but by the decay of other heavier dark sector particles which on the other hand can be produced by the thermal freeze-out mechanism. Using a concrete model with a light dark matter from dark sector decay, we study the collider signature of the dark sector particles in association with Higgs production processes. We find that the future lepton colliders can be a better place to probe the signature of this kind of light dark matter model than the hadron collider such as LHC. Meanwhile, it is found that a Higgs factory with center of mass energy 250 GeV has a better potential to resolve the signature of this kind of light dark matter model than the Higgs factory with center of mass energy 350 GeV.Comment: 15 pages, 14 figure

Refunctionalizing a Frayed American China-Taiwan Policy: Incrementalism or Paradigmatic Shift?

This paper is interested in exploring whether it is possible for the US. to pursue parallel relationships with Taiwan and China, that is, whether US.-Taiwan relations can be decoupled from the Washington-Beijing relationship? This paper uses a spatial model to review how US-Taiwan relations have evolved since 1949, when the reality of two Chinas set in with the founding of the PRC. It discusses the increasingly unbalanced dual track framework of current US. policy toward China and Taiwan and contrasts the changing contexts between the SCP\u27s time and the present post-Cold War era. It examines those most important new parameters that were absent or different in the SCP. Based on this contrast, the paper questions the policy\u27s continued validity and calls for a new paradigm to replace the SCP. Based on these new parameters, the final section sketches out a new paradigm for US. policy toward Taiwan in the post-Cold War era and weighs the pros and cons of three distinct policy choices - disengagement, decoupling, and improved status quo-for the shape and direction of future US.-Taiwan relations. By bringing developments up to date (President Bush\u27s December 9, 2003 comments regarding Taiwan\u27s referendum), this paper argues that although the Bush Administration seems content to refunctionalize a frayed framework, it has abandoned strategic ambiguity and has added preference for the status quo

Resource Management in Cloud-based Radio Access Networks: a Distributed Optimization Perspective

University of Minnesota Ph.D. dissertation. 2015. Major: Electrical Engineering. Advisor: Zhi-Quan Luo. 1 computer file (PDF); ix, 136 pages.In this dissertation, we consider the base station (BS) and the resource management problems for the cloud-based radio access network (C-RAN). The main difference of the envisioned future 5G network architecture is the adoption of multi-tier BSs to extend the coverage of the existing cellular BSs. Each of the BS is connected to the multi-hop backhaul network with limited bandwidth. For provisioning the network, the cloud centers have been proposed to serve as the control centers. These differences give rise to many practical challenges. The main focus of this dissertation is the distributed strategy across the cloud centers. First, we show that by jointly optimizing the transceivers and determining the active set of BSs, high system resource utilization can be achieved with only a small number of BSs. In particular, we provide efficient distributed algorithms for such joint optimization problem, under the following two common design criteria: i) minimization of the total power consumption at the BSs, and ii) maximization of the system spectrum efficiency. In both cases, we introduce a nonsmooth regularizer to facilitate the activation of the most appropriate BSs, and the algorithms are, respectively, developed with Alternating Direction Method of Multipliers (ADMM) and weighted minimum mean square error (WMMSE) algorithm. In the second part, we further explicitly consider the backhaul limitation issues. We propose an efficient algorithm for joint resource allocation across the wireless links and the flow control over the entire network. The algorithm, which maximizes the utility function of the rates among all the transmitted commodities, is based on a decomposition approach leverages both the ADMM and the WMMSE algorithms. This algorithm is shown to be easily parallelizable within cloud centers and converges globally to a stationary solution. Lastly, since ADMM has been popular for solving large-scale distributed convex optimization, we further consider the issues of the network synchronization across the cloud centers. We propose an ADMM-type implementation that can handle a specific form of asynchronism based on the so-called BSUM-M algorithm, a new variant of ADMM. We show that the proposed algorithm converges to the global optimal solution

On-chip electro-optic tuning of a lithium niobate microresonator with integrated in-plane microelectrodes

We demonstrate electro-optic tuning of an on-chip lithium niobate microresonator with integrated in-plane microelectrodes. First two metallic microelectrodes on the substrate were formed via femtosecond laser process. Then a high-Q lithium niobate microresonator located between the microelectrodes was fabricated by femtosecond laser direct writing accompanied by focused ion beam milling. Due to the efficient structure designing, high electro-optical tuning coefficient of 3.41 pm/V was observed.Comment: 6 pages, 3 figure