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This paper considers the decentralized optimization problem, where agents in a network cooperate to minimize the sum of their local objective functions by communication and local computation. We propose a decentralized second-order communication-efficient algorithm called communication-censored and communication-compressed quadratically approximated alternating direction method of multipliers (ADMM), termed as CC-DQM, by combining event-triggered communication with compressed communication. In CC-DQM, agents are allowed to transmit the compressed message only when the current primal variables have changed greatly compared to its last estimate. Moreover, to relieve the computation cost, the update of Hessian is also scheduled by the trigger condition. Theoretical analysis shows that the proposed algorithm can still maintain an exact linear convergence, despite the existence of compression error and intermittent communication, if the local objective functions are strongly convex and smooth. Finally, numerical experiments demonstrate its satisfactory communication efficiency. [ABSTRACT FROM AUTHOR]

In this paper, elliptic optimal control problems with L 1 -control cost and box constraints on the control are considered. To numerically solve the optimal control problems, we use the First optimize, then discretize approach. We focus on the inexact alternating direction method of multipliers (iADMM) and employ the standard piecewise linear finite element approach to discretize the subproblems in each iteration. However, in general, solving the subproblems is expensive, especially when the discretization is at a fine level. Motivated by the efficiency of the multigrid method for solving large-scale problems, we combine the multigrid strategy with the iADMM algorithm. Instead of fixing the mesh size before the computation process, we propose the strategy of gradually refining the grid. Moreover, to overcome the difficulty whereby the L 1 -norm does not have a decoupled form, we apply nodal quadrature formulas to approximately discretize the L 1 -norm and L 2 -norm. Based on these strategies, an efficient multilevel heterogeneous ADMM (mhADMM) algorithm is proposed. The total error of the mhADMM consists of two parts: the discretization error resulting from the finite-element discretization and the iteration error resulting from solving the discretized subproblems. Both errors can be regarded as the error of inexactly solving infinite-dimensional subproblems. Thus, the mhADMM can be regarded as the iADMM in function space. Furthermore, theoretical results on the global convergence, as well as the iteration complexity results o (1 / k) for the mhADMM, are given. Numerical results show the efficiency of the mhADMM algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers' wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models. [ABSTRACT FROM AUTHOR]

In the present paper, we propose two new methods for tensor completion of third-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function, namely the tensor nuclear norm. The recovered data will be obtained by combining the minimization process with the total variation regularization technique. We will adopt the alternating direction method of multipliers, using the tensor T-product, to solve the main optimization problems associated with the two proposed algorithms. In the last section, we present some numerical experiments and comparisons with the most known image video completion methods. [ABSTRACT FROM AUTHOR]

Since the established wind farms (WFs) have a strong demand for reducing maintenance costs, the fatigue load suppression of wind turbines (WTs) has become more important in WFs. To suppress the fatigue load during operation, the traditional schemes are tried by allocating the optimized power setting value to each WT, which does not directly point to the key operating parameters that affect fatigue. In response to this, an advanced WT control model with two-degree-of-freedom (2Dof) is applied in this paper to ensure that the generator torque and pitch angle (two key parameters affecting fatigue load) of each WT are directly controlled. In order to achieve effective control of the above two parameters in multiple WTs, a hierarchical distributed control architecture with dynamic-local-reference is proposed to jointly optimize the above two configurable parameters at both the WT and WF levels. Several cases are compared to verify the proposed method, and simulation results show that the proposed 2Dof control model for WT and distributed control framework for WF can significantly reduce the fatigue load of each WT while completing the active power command of the whole WF. • Two-degree-of-freedom wind turbine control model is applied in wind farms. • Distributed model predictive control (DMPC) framework is adopted. • Dynamic WT reference power algorithm is proposed based on DMPC. • Fatigue load of all wind turbines in the wind farm are significantly reduced. [ABSTRACT FROM AUTHOR]

Total variation (TV) and non-local self-similarity (NSS) are powerful tools for successfully enhancing compressive sensing performance. However, standard TV approaches often over-smooth detailed edges in the image, due to the uniform regularization of gradient magnitude. In this paper, a novel compressed sensing method for the reconstruction of medical images is proposed, the image edges are well preserved with the proposed reweighted TV. The redundancy of the NSS patch also is leveraged through the sparse regression model. The proposed model was solved with an efficient strategy of the Alternating Direction Method of Multipliers (ADMM) algorithm. Experimental results on thesimulated phantom, brain Magnetic resonance imaging (MRI) show that the proposed method outperforms the state-of-the-art compressed sensing approaches. [ABSTRACT FROM AUTHOR]

Tensor principal component pursuit (TPCP) is a powerful approach in the tensor robust principal component analysis (TRPCA), where the goal is to decompose a data tensor to a low-tubal-rank part plus a sparse residual. TPCP is shown to be effective under certain tensor incoherence conditions, which can be restrictive in practice. In this paper, we propose a Modified-TPCP, which incorporates the prior subspace information in the analysis. With the aid of prior info, the proposed method is able to recover the low-tubal-rank and the sparse components under a significantly weaker incoherence assumption. We further design an efficient algorithm to implement Modified-TPCP based upon the alternating direction method of multipliers (ADMM). The promising performance of the proposed method is supported by simulations and real data applications. [ABSTRACT FROM AUTHOR]

In this paper, we develop a robust conditional value at risk (CVaR) optimal portfolio rebalancing model under various financial constraints to construct sparse and diversified rebalancing portfolios. Our model includes transaction costs and double cardinality constraints in order to capture the trade-off between the limit of investment scale and the diversified industry coverage requirement. We first derive a closed-form solution for the robust CVaR portfolio rebalancing model with only transaction costs. This allows us to conduct an industry risk analysis for sparse portfolio rebalancing in the absence of diversification constraints. Then, we attempt to remedy the hidden industry risk by establishing a new robust portfolio rebalancing model with both sparse and diversified constraints. This is followed by the development of a distributed-version of the Alternating Direction Method of Multipliers (ADMM) algorithm, where each subproblem admits a closed-form solution. Finally, we conduct empirical tests to compare our proposed strategy with the standard sparse rebalancing and no-rebalancing strategies. The computational results demonstrate that our rebalancing approach produces sparse and diversified portfolios with better industry coverage. Additionally, to measure out-of-sample performance, two superiority indices are created based on worst-case CVaR and annualized return, respectively. Our ADMM strategy outperforms the sparse rebalancing and no-rebalancing strategies in terms of these indices. [ABSTRACT FROM AUTHOR]

Optimization algorithms play a significant role in the optimal solution of various problems in Smart Grid. Distributed algorithms are of considerable research interest as these algorithms replace the centrally computed algorithms. This paper surveys the literature on the Alternating Direction Method of Multipliers (ADMM) algorithm, its versions and their applications in Smart grid operation and control, particularly in Optimal Power Flow (OPF), Economic Dispatch (ED), Demand Response (DR), pricing mechanism, Electric Vehicles (EVs), Cyber–Physical Systems (CPS), Multi Energy Systems (MES), Peer to Peer (P2P) trading, resilience, forecast techniques, State Estimation (SE), and some miscellaneous topics. This paper presented research gaps and future directions on all these applications in smart grids. Furthermore, it provided a joint research gap on all these applications, such as the impact of communication failures or communication delays, effect of uncertainties, incorporating the fraudulent behaviour of participants, usage of Blockchain technology, implementation of smart contract on the performance of these algorithms. Furthermore, the work has developed a decentralized and distributed automatic electricity trading mechanism for the independent microgrid without needing a central aggregator. • The paper "A Survey on Applications of Alternating Direction Method of Multipliers in Smart Power Grids" presents a wide range of literature on Optimization algorithms, especially the ADMM and its applications in the smart grid. • Also discussed the detailed overview of optimization algorithms and how the requirement of power systems has evolved from centralized to distributed algorithms. • Furthermore, it provided a joint research gap on all the applications, such as the impact of communication failures or delays, uncertainties, fraudulent behaviour of participants, and usage of Blockchain technology. • Moreover, authors developed an automatic decentralized and distributed electricity trading environment using smart contracts written on blockchain. [ABSTRACT FROM AUTHOR]

• Develop an effective and efficient ADMM solver for sparse phase retrieval with convergence guarantee. • Though the problem is nonconvex, the solver numerically solves it without requirement of good initialization. • The solver outperforms existing solvers in terms of the required measurement complexity. Phase retrieval, as a representative nonlinear inverse problem, is of increasing interest recently for its broad applications in imaging and engineering. Prediction of the signal amounts to solving a nonconvex optimization problem, which is generally NP-hard to solve. Collecting more measurements or providing prior information of the unknown are two often-seen strategies to facilitate the problem. In this paper, we propose an efficient and effective algorithm to solve phase retrieval with certain prior of the signal, in particular the signal itself is sparse in the natural basis. By formulating phase retrieval (PR) problem in the splitting form, we propose ADMM (alternating direction method of multipliers) with convergence guarantee to tackle the resulting nonconvex problem. Even though the algorithm is not new and there also exist several works on the convergence of ADMM, we clarify that our formulation for phase retrieval is not a specific application example of their investigated models. Hence, we investigate the convergence of our algorithm and show that ADMM converges a stationary point when penalty parameter ρ is large enough. It is observed that the recovery performance degrades when the penalty parameter increases. For better performance, we propose a practical scheme of tuning the penalty parameter ρ. Demonstration of the superior recovery performance on sparse phase retrieval (SPR) is conducted and it shows that our method numerically infers near-exact solution without providing good initialization. Our proposed method distinguishes itself from other existing competitive algorithms in two aspects: (a) the initialization is much less crucial for the algorithmic success than other compared methods; (b) the sampling complexity for the phase transition of recovery is much markedly reduced than other existing methods. [ABSTRACT FROM AUTHOR]

• A low-rank plus sparse tensor model to decompose the urban traffic data into normal and anomalous components. • Imposed temporal smoothness on the sparse part of the tensor through total variation regularization. • Introduced graph regularization to exploit the geometric structure of the data. • Solve a tensor completion problem simultaneously with the anomaly detection problem. • The resulting spatiotemporal features can be scored by any conventional anomaly scoring algorithm. Anomaly detection in spatiotemporal data is a problem encountered in a variety of applications including urban traffic monitoring. For urban traffic data, anomalies refer to unusual events such as traffic congestion and unexpected crowd gatherings. Detecting these anomalies is challenging due to the scarcity of anomalous events and the dependence of anomaly definition on time and space. Existing spatiotemporal anomaly detection methods cannot preserve the spatial and temporal correlations and do not take the structure of anomalies into account. In this paper, we introduce a temporally regularized, locally consistent, robust low-rank plus sparse tensor model for spatiotemporal anomaly detection. The proposed method takes the spatially sparse and temporally smooth structure of urban anomalies into account by modeling the anomalies as the sparse part of the tensor and minimizing the total variation across the temporal mode of this part. The local consistency of the low-rank part is ensured using a manifold embedding approach. The proposed approach is referred to as Graph Regularized Low-rank plus Temporally Smooth Sparse decomposition (GLOSS) and is evaluated on synthetic and real spatiotemporal urban traffic data. The results illustrate the accuracy and robustness of the proposed method with respect to missing data, noise and anomaly strength. [ABSTRACT FROM AUTHOR]