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Aiming at solving large-scale optimization problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the optimization 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-ADMM) 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 the standard convex setting.

Random laser with intrinsically uncomplicated fabrication processes, high spectral radiance, angle-free emission, and conformal onto freeform surfaces is in principle ideal for a variety of applications, ranging from lighting to identification systems. In this work, a white random laser (White-RL) with high-purity and high-stability is designed, fabricated, and demonstrated via the cost-effective materials (e.g., organic laser dyes) and simple methods (e.g., all-solution process and self-assembled structures). Notably, the wavelength, linewidth, and intensity of White-RL are nearly isotropic, nevertheless hard to be achieved in any conventional laser systems. Dynamically fine-tuning colour over a broad visible range is also feasible by on-chip integration of three free-standing monochromatic laser films with selective pumping scheme and appropriate colour balance. With these schematics, White-RL shows great potential and high application values in high-brightness illumination, full-field imaging, full-colour displays, visible-colour communications, and medical biosensing.

The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension is large, a distributed version of ADMM can be used, which is capable of distributing the computation load and the data set to a network of computing nodes. Unfortunately, a direct synchronous implementation of such algorithm does not scale well with the problem size, as the algorithm speed is limited by the slowest computing nodes. To address this issue, in a companion paper, we have proposed an asynchronous distributed ADMM (AD-ADMM) and studied its worst-case convergence conditions. In this paper, we further the study by characterizing the conditions under which the AD-ADMM achieves linear convergence. Our conditions as well as the resulting linear rates reveal the impact that various algorithm parameters, network delay and network size have on the algorithm performance. To demonstrate the superior time efficiency of the proposed AD-ADMM, we test the AD-ADMM on a high-performance computer cluster by solving a large-scale logistic regression problem.

An integrated random laser based on green materials with dissolubility and recyclability is created and demonstrated. The dissolvable and recyclable random laser (DRRL) can be dissolved in water, accompanying the decay of emission intensity and the increment in lasing threshold. Furthermore, the DRRL can be reused after the process of deionized treatment, exhibiting excellent reproducibility with several recycling processes.