Proximal gradient-based step for brain distributed epileptic source imaging after tensor decomposition preprocessing

In the field of ultrasonic nondestructive testing (NDT), robust and accurate detection of defects is a challenging task because of the attenuation and noising of the ultrasonic wave from the structure. For determining the reflection characteristics representing the position and amplitude of ultrasonic detection signals, sparse blind deconvolution methods have been implemented to separate overlapping echoes when the ultrasonic transducer impulse response is unknown. This letter introduces the ratio regularization function to model the deconvolution as a nonconvex optimization problem. The initialization influences the accuracy of estimation and, for this purpose, the alternating direction method of multipliers (ADMM) combined with blind gain calibration is used to find the initial approximation to the real solution, given multiple observations in a joint sparsity case. The proximal alternating linearized minimization (PALM) algorithm is embedded in the iterate solution, in which the majorize-minimize (MM) approach accelerates convergence. Compared with conventional blind deconvolution algorithms, the proposed methods demonstrate the robustness and capability of separating overlapping echoes in the context of synthetic experiments.

Distributed machine learning has gained lots of attention due to the rapid growth of data. In this paper, we focus regularized empirical risk minimization problems, and propose two novel Distributed Accelerated Alternating Direction Method of Multipliers (D-A2DM2) algorithms for distributed classification. Based on the framework of Alternating Direction Method of Multipliers (ADMM), we decentralize the distributed classification problem as a global consensus optimization problem with a series of sub-problems. In D-A2DM2, we exploit ADMM with variance reduction for sub-problem optimization in parallel. Taking global update and local update into consideration respectively, we propose two acceleration mechanisms in the framework of D-A2DM2. In particular, inspired by Nesterov's accelerated gradient descent, we utilize it for global update to further improve time efficiency. Moreover, we also introduce Nesterov's acceleration for local update, and develop the corrected local update and symmetric dual update to accelerate the convergence with only a little change in the computational effort. Theoretically, D-A2DM2 has a linear convergence rate. Empirically, experimental results show that D-A2DM2 converge faster than existing distributed ADMM-based classification, and could be a highly efficient algorithm for practical use.

In recent years, the combined cooling, heating and power (CCHP) system has attracted increasing attention. However, due to data privacy, it is challenging to exchange detailed topology or operation states between electric power system (EPS) and district heating and cooling (DHC) system, so it is necessary to carry out distributed optimization for the CCHP system dispatch problem. This paper is focused on CCHP system dispatch problem and first establishes its mathematical model. Then, based on the relaxed alternating direction method of multipliers (R-ADMM) algorithm, this paper proposes the adaptive step-size R-ADMM algorithm using the strategy of adaptive step-size to reduce iteration times. Simulation results show that the adaptive step-size R-ADMM algorithm can significantly reduce the number of iteration times compared with the classic alternating direction method of multipliers (ADMM).

Data collection plays an important role in wireless sensor networks. Recovery of spatio-temporal data from incomplete sensing data is vital to the network lifetime. Many works have utilized the spatial and temporal correlations to achieve satisfactory data recovery results. However, these methods introduce large computational overhead at the fusion center. In this paper, we develop an ADMM-Net framework for correlated spatio-temporal data recovery. Both the spatial correlation and temporal correlation of sensing data are considered in a convex optimization problem, which is solved by the alternating direction method of multipliers (ADMM) algorithm. We then unfold the ADMM algorithm into a fixed-length neural network that reduces the iterations dramatically and does not require additional location information of nodes. Experimental results on a realworld dataset demonstrate that the proposed method can achieve faster convergence speed than the baseline ADMM algorithm with slight accuracy loss.

A survey on applications of Alternating Direction Method of Multipliers in smart power grids

This paper examines simultaneous design of the network topology and the corresponding edge weights in the presence of a cardinality constraint on the edge set. Network properties of interest for this design problem lead to optimization formulations with convex objectives, convex constraint sets, and cardinality constraints. This class of problems is referred to as the cardinality-constrained optimization problem (CCOP); the cardinality constraint generally makes CCOPs NP-hard. In this paper, a customized alternating direction method of multipliers (ADMM) algorithm aiming to improve the scalability of the solution strategy for large-scale CCOPs is proposed. This algorithm utilizes the special structure of the problem formulation to obtain closed-form solutions during each iterative step of the corresponding ADMM updates. We also provide a convergence proof of the proposed customized ADMM to a stationary point under certain conditions. Simulation results illustrate that the customized ADMM algorithm has a significant computational advantage over existing methods, particularly for large-scale network design problems.

Generation following with thermostatically controlled loads via alternating direction method of multipliers sharing algorithm

We focus on the problem of minimizing a finite sum f(x) = Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">=</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (x) of n functions f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , where f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> are convex and available only locally to an agent i. The n agents are connected in a directed network G (V, E). In this article, we present the Directed-Distributed Alternating Direction Method of Multiplier (D-DistADMM) Algorithm, which is an Alternating Direction Method of Multiplier (ADMM) based scheme and utilizes a finite-time "approximate" consensus method to solve the above optimization problem distributively. At each iteration of the proposed scheme the agents solve their local optimization problem and utilize an approximate consensus protocol to update a local estimate of the global optimization variable. We show that for convex and not-necessarily differentiable objective functions the proposed D-DistADMM method converges at a rate O(1/k), where k is the iteration counter, in terms the difference between the Lagrangian function evaluated at any iteration k of the D-DistADMM algorithm and the optimal solution. We further demonstrate the features of our algorithm by solving a distributed least squares problem.

Nowadays, the entire world faces challenges in energy and environment. To resolve these problems, the power systems are interconnected to promote the development of renewable energy sources (RESs). However, the economic dispatch problem for the global energy interconnection (GEI) should tackle two issues: 1) handle the uncertainty from RES and allocate the responsibility among the interconnected countries; 2) protect the information privacy through the dispatch. Motivated by the above, this paper proposes a zonally adjustable robust decentralized economic dispatch model for the GEI. In the model, each country is only responsible for its own uncertainty, and tie-line power flows remain unchanged under uncertainties. Moreover, an alternating direction method of multipliers (ADMM)-based fully distributed algorithm is utilized, in which only limited information should be exchanged between neighbor countries. Finally, a case study on the Northeast Asian countries verifies the effectiveness of the proposed method.

Features and interaction between features of liver disease is of great significance for the classification of liver disease. Based on least absolute shrinkage and selection operator (LASSO) and interaction LASSO, the generalized interaction LASSO model is proposed in this paper for liver disease classification and compared with other methods. Firstly, the generalized interaction logistic classification model was constructed and the LASSO penalty constraints were added to the interactive model parameters. Then the model parameters were solved by an efficient alternating directions method of multipliers (ADMM) algorithm. The solutions of model parameters were sparse. Finally, the test samples were fed to the model and the classification results were obtained by the largest statistical probability. The experimental results of liver disorder dataset and India liver dataset obtained by the proposed methods showed that the coefficients of interaction features of the model were not zero, indicating that interaction features were contributive to classification. The accuracy of the generalized interaction LASSO method is better than that of the interaction LASSO method, and it is also better than that of traditional pattern recognition methods. The generalized interaction LASSO method can also be popularized to other disease classification areas.

This paper presents a convergence analysis on a distributed Alternating Direction Method of Multipliers (ADMM) algorithm which solves online convex optimization problems under linear constraints. The goal is to distributively optimize a global objective function over a network of decision makers. The global objective function is composed of convex cost functions associated with each agent. The local cost functions can be broken down into two convex functions, one of which is revealed over time to the decision makers and one known a priori. We extend an online ADMM algorithm to a distributed setting based on dual-averaging. We then explore the rate of convergence of the performance of the sequence of decisions generated by the algorithm to the best fixed decision in hindsight. This performance metric is called regret. An upper bound on the regret of the proposed algorithm is presented as a function of the underlying network topology and linear constraints. The online distributed ADMM algorithm is then applied to a formation acquisition problem.

The decentralized approach is popular for the collaborative collision avoidance of connected vehicles in many scenarios. By modeling the task as a collaborative optimal control problem, Lagrangian methods are widely used to decouple the constraints and enable the decentralized solution. However, potential constraint-violating behavior will lead to oscillations during the Lagrangian update, resulting in more iterations and lower real-time efficiency. Existing methods generally neither address this shortcoming, nor explore the Lagrangian update mechanism. This study takes a control perspective, and solves this collaborative optimal control problem based on an extension of the Alternating Directions Method of Multipliers (ADMM) algorithm by performing the iteration update with a Proportional-Integral-(PI-) regulated controller. The link between the Lagrangian optimization and the PI controller improves the convergence performance during iterations. Simulation results in traffic intersection scenarios demonstrate the advantage of the proposed approach.

An essential aspect that contributes to the resilience of radial electrical distribution systems (EDS) is the deployment of efficient and fast service restoration methods. In the presence of a permanent fault, the service restoration minimizes the amount of de-energized consumers by reducing the area that needs to be disconnected to isolate the faulty section of the network. To do so, the service restoration algorithm can make use of automated switching devices and dispatchable energy resources allocated throughout the network to transfer loads among feeders, considering the system's operational constraints. Depending on the size of the system and the complexity of the telecommunication infrastructure, the application of centralized restoration systems may neither be practical nor flexible. Thus, in this paper, a distributed service restoration method is proposed, using the alternating direction method of multipliers (ADMM) algorithm to solve the optimization problem. As such, the original service restoration model is distributed among the nodes and branches of the system that exchange limited information with neighboring nodes and branches. Radiality constraint is also distributed by the proposed ADMM algorithm. A 44-node test system was used to conduct case studies. Results demonstrate that the proposed method efficiently solves the service restoration in active EDS without using a centralized Intelligence.

Park-level integrated energy internet (PEI), a multiple energy coupling and obvious zoning system, is set up to meet the growing demand of energy consumption and improve the comprehensive utilization efficiency of multiple energy resources. Traditional distributed alternating direction method of multipliers (ADMM) algorithm with a control center holding all information is often used to solve the dispatch model of PEI, which may cause security problems. In this article, we use the parallel ADMM algorithm to solve the problem in a distributed way. Meanwhile, a completely distributed scheme based on the average-consensus parallel ADMM algorithm is designed to eliminate the computing center of the subregion. The simulation results verified the validity of the proposed method.

This paper proposes a decentralized alternating direction method of multipliers (ADMM) algorithm for solving the optimization problem of energy scheduling in microgrids. Different from the other ADMM-based distributed approaches which decomposes the monolithic problem spatially into smaller tractable subproblems, the proposed method adopts a temporal decomposition on the scenario tree inherited from multi-stage stochastic programming. Each node in the scenario tree serves its own optimization with local variables and constraints, and iteratively updates information with adjacent nodes. By implementing the proposed ADMM algorithm in a rolling fashion, simulation results have shown the fast convergence of the temporal distribution framework, and comparisons on optimal value and computation time with other optimization approaches reveals its advantages and effectiveness.