In this letter, a novel projection algorithm is proposed in which projection onto a triangle consisting of the three even-vertices closest to the vector to be projected replaces check polytope projection, achieving the same FER performance as exact projection algorithm in both high-iteration and low-iteration regime. Simulation results show that compared with the sparse affine projection algorithm (SAPA), it can improve the FER performance by 0.2 dB as well as save average number of iterations by 4.3%.

In a power network, it is important to detect a cyber attack. In this paper, we propose a method for detecting false data injection (FDI) attacks in distributed state estimation. An FDI attack is well known as one of the typical cyber attacks in a power network. As a method of FDI attack detection, we consider calculating the residual (i.e., the difference between the observed and estimated values). In the proposed detection method, the tentative residual (estimated error) in ADMM (Alternating Direction Method of Multipliers), which is one of the powerful methods in distributed optimization, is applied. First, the effect of an FDI attack is analyzed. Next, based on the analysis result, a detection parameter is introduced based on the residual. A detection method using this parameter is then proposed. Finally, the proposed method is demonstrated through a numerical example on the IEEE 14-bus system.

The Euclidean projection operation is the most complex and time-consuming of the alternating direction method of multipliers (ADMM) decoding algorithms, resulting in a large number of resources when deployed on hardware platforms. We propose a simplified line segment projection algorithm (SLSA) and present the hardware design and the quantization scheme of the SLSA. In simulation results, the proposed SLSA module has a better performance than the original algorithm with the same fixed bitwidths due to the centrosymmetric structure of SLSA. Furthermore, the proposed SLSA module with a simpler structure without hypercube projection can reduce time consuming by up to 72.2% and reduce hardware resource usage by more than 87% compared to other Euclidean projection modules in the experiments.

Design of distributed energy management systems composed of several agents such as factories and buildings is important for realizing smart cities. In addition, demand response for saving the power consumption is also important. In this paper, we propose a design method of distributed energy management systems with real-time demand response, in which both electrical energy and thermal energy are considered. Here, we use ADMM (Alternating Direction Method of Multipliers), which is well known as one of the powerful methods in distributed optimization. In the proposed method, demand response is performed in real-time, based on the difference between the planned demand and the actual value. Furthermore, utilizing a blockchain is also discussed. The effectiveness of the proposed method is presented by a numerical example. The importance of introducing a blockchain is pointed out by presenting the adverse effect of tampering the actual value.

The unit commitment problem (UCP) is the problem of deciding up/down and generation-level patterns of energy production units. Due to the expansion of distributed energy resources and the liberalization of energy trading in recent years, solving the distributed UCP (DUCP) is attracting the attention of researchers. Once an up/down pattern is determined, the generation-level pattern can be decided distributively using the alternating direction method of multipliers (ADMM). However, ADMM does not guarantee convergence when deciding both up/down and generation-level patterns. In this paper, we propose a method to solve the DUCP using ADMM and constraint optimization programming. Numerical experiments show the efficacy of the proposed method.

Linear programming (LP) decoding based on the alternating direction method of multipliers (ADMM) has proved to be effective for low-density parity-check (LDPC) codes. However, for high-density parity-check (HDPC) codes, the ADMM-LP decoder encounters two problems, namely a high-density check matrix in HDPC codes and a great number of pseudocodewords in HDPC codes' fundamental polytope. The former problem makes the check polytope projection extremely complex, and the latter one leads to poor frame error rates (FER) performance. To address these issues, we introduce the even vertex algorithm (EVA) into the ADMM-LP decoding algorithm for HDPC codes, named as HDPC-EVA. HDPC-EVA can reduce the complexity of the projection process and improve the FER performance. We further enhance the proposed decoder by the automorphism groups of codes, creating diversity in the parity-check matrix. The simulation results show that the proposed decoder is capable of cutting down the average decoding time for each iteration by 30%-60%, as well as achieving near maximum likelihood (ML) performance on some BCH codes.

A blockchain, which is well known as one of the distributed ledgers, has attracted in many research fields. In this paper, we discuss the effectiveness and limitation of a blockchain in distributed optimization. In distributed optimization, the original problem is decomposed, and the local problems are solved by multiple agents. In this paper, ADMM (Alternating Direction Method of Multipliers) is utilized as one of the powerful methods in distributed optimization. In ADMM, an aggregator is basically required for collecting the computation result in each agent. Using blockchains, the function of an aggregator can be contained in a distributed ledger, and an aggregator may not be required. As a result, tampering from attackers can be prevented. As an application, we consider energy management systems (EMSs). By numerical experiments, the effectiveness and limitation of blockchain-based distributed optimization are clarified.

The combination of large-scale antenna arrays and simultaneous wireless information and power transfer (SWIPT), which can provide enormous increase of throughput and energy efficiency is a promising key in next generation wireless system (5G). This paper investigates efficient transceiver design to minimize transmit power, subject to users' required data rates and energy harvesting, in large-scale SWIPT system where the base station utilizes a very large number of antennas for transmitting both data and energy to multiple users equipped with time-switching (TS) or power-splitting (PS) receive structures. We first propose the well-known semidefinite relaxation (SDR) and Gaussian randomization techniques to solve the minimum transmit power problems. However, for these large-scale SWIPT problems, the proposed scheme, which is based on conventional SDR method, is not suitable due to its excessive computation costs, and a consensus alternating direction method of multipliers (ADMM) cannot be directly applied to the case that TS or PS ratios are involved in the optimization problem. Therefore, in the second solution, our first step is to optimize the variables of TS or PS ratios, and to achieve simplified problems. After then, we propose fast algorithms for solving these problems, where the outer loop of sequential parametric convex approximation (SPCA) is combined with the inner loop of ADMM. Numerical simulations show the fast convergence and superiority of the proposed solutions.

Existing image deblurring methods with a blurred/noisy image pair take a two-step approach: blur kernel estimation and image restoration. They can achieve better and much more stable blur kernel estimation than single image deblurring methods. On the other hand, in the image restoration step, they do not exploit the information on the noisy image, or they require ad hoc tuning of interdependent parameters. This paper focuses on the image restoration step and proposes a new restoration method of using a blurred/noisy image pair. In our method, the image restoration problem is formulated as a constrained convex optimization problem, where data-fidelity to a blurred image and that to a noisy image is properly taken into account as multiple hard constraints. This offers (i) high quality restoration when the blurred image also contains noise; (ii) robustness to the estimation error of the blur kernel; and (iii) easy parameter setting. We also provide an efficient algorithm for solving our optimization problem based on the so-called alternating direction method of multipliers (ADMM). Experimental results support our claims.

State-of-the-art background subtraction and foreground detection methods still face a variety of challenges, including illumination changes, camouflage, dynamic backgrounds, shadows, intermittent object motion. Detection of foreground elements via the robust principal component analysis (RPCA) method and its extensions based on low-rank and sparse structures have been conducted to achieve good performance in many scenes of the datasets, such as Changedetection.net (CDnet); however, the conventional RPCA method does not handle shadows well. To address this issue, we propose an approach that considers observed video data as the sum of three parts, namely a row-rank background, sparse moving objects and moving shadows. Next, we cast inequality constraints on the basic RPCA model and use an alternating direction method of multipliers framework combined with Rockafeller multipliers to derive a closed-form solution of the shadow matrix sub-problem. Our experiments have demonstrated that our method works effectively on challenging datasets that contain shadows.

Solving image recovery problems requires the use of some efficient regularizations based on a priori information with respect to the unknown original image. Naturally, we can assume that an image is modeled as the sum of smooth, edge, and texture components. To obtain a high quality recovered image, appropriate regularizations for each individual component are required. In this paper, we propose a novel image recovery technique which performs decomposition and recovery simultaneously. We formulate image recovery as a nonsmooth convex optimization problem and design an iterative scheme based on the alternating direction method of multipliers (ADMM) for approximating its global minimizer efficiently. Experimental results reveal that the proposed image recovery technique outperforms a state-of-the-art method.