Fast Alternating Direction Method Of Multipliers Research Articles

Robust Support Vector Data Description with Truncated Loss Function for Outliers Depression.

Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework into the SVDD model to enhance its robustness and employs the fast alternating direction method of multipliers (ADMM) algorithm to solve various truncated loss functions. Moreover, the convergence of the fast ADMM algorithm is analyzed theoretically. Within this framework, we developed the truncated generalized ramp, truncated binary cross entropy, and truncated linear exponential loss functions for SVDD. We conducted extensive experiments on synthetic and real-world datasets to validate the effectiveness of these three SVDD models in handling data with different noise levels, demonstrating their superior robustness and generalization capabilities compared to other SVDD models.

Crafting a decentralized framework for energy sharing among smart homes in a peer-to-peer market

In this paper, a new framework for the participation of smart homes in the peer-to-peer energy market is presented, in which smart homes share their surplus energy with each other to maintain the balance between generation and demand through bilateral trading. The seller smart homes, players who always sell their excess energy to the buyer smart homes in the peer-to-peer market, are equipped with distributed energy resources including electric vehicles, power-only units, and uncontrollable loads. The buyer smart homes always interact with sellers as energy consumers to supply their flexible loads. The presence of battery energy storage systems in the model of these players, as well as active participation in load response programs, increases the flexibility and profit obtained from energy transactions. All players regardless of their role in the peer-to-peer market, have bilateral trading with the retail market considering real-time energy pricing rates to gain more profit. A fully decentralized method called the Fast Alternating Direction Method of multipliers (FADMM) is used to clear the developed market. To prove the effectiveness of the proposed framework, numerical studies are considered for the energy transactions of several smart homes with each other and with the retail market.

Asymmetric Nash bargaining-based cooperative energy trading of multi-park integrated energy system under carbon trading mechanism

This paper proposes an asymmetric Nash bargaining-based cooperative operation strategy for a multi-park integrated energy system (MPIES). During the design process, the model for each PIES is firstly constructed. Then, based on the Nash bargaining theory and carbon trading mechanism, a cooperative operation model is proposed to determine optimal power trading in the MPIES. To mitigate computational complexity, the designed non-convex and non-linear Nash bargaining problem is transformed into two subproblems. Particularly, an asymmetric bargaining-based method is incorporated within the benefit allocation maximization subproblem such that an equitable allocation of benefits can be achieved. In order to protect the privacy of each PIES, a distributed approach is designed for the proposed optimization problem, where the Fast-alternating direction method of multipliers (Fast-ADMM) algorithm is employed such that the calculation time is short enough to track the fast time-varying operation condition. The case study results show that, within an MPIES comprising three PIESs, with the proposed energy trading scheme, the operating cost of each PIES can be reduced by 13.52 %, 4.75 %, and 13.39 %, respectively, while the overall carbon emissions can be reduced by 7.9 %. The effectiveness of the proposed method is also validated through its application in a larger practical MPIES.

Fast alternating direction algorithms for sparse portfolio model via sorted ℓ1-norm

In this paper, we propose two novel Alternating Direction Method of Multipliers (ADMM) algorithms for the sparse portfolio problem via sorted ℓ1-norm penalization (SLOPE). The first algorithm (FADMM) is presented by adding a prediction-correction step to the classic ADMM framework. Since the problem is not strongly convex, the second fast ADMM (FADMMR) is proposed by utilizing both prediction-correction step and restarting rules. Numerical experiments show that the FADMMR algorithm converges faster than the FADMM algorithm and ADMM algorithm when tuning parameters are relatively small. On the other hand, when tuning parameters are relative large, the FADMM algorithm performs better than the FADMMR algorithm and ADMM algorithm. The FADMM algorithm and FADMMR algorithm converge faster than the ADMM algorithm in terms of convergence time for different sizes of tuning parameters. For large-scale portfolio problem, the proposed algorithms have highly performance as well. Finally, empirical analysis on five datasets of stocks index show that the proposed algorithms are efficient and superior for solving sparse portfolio problems via SLOPE.

A Robust Decentralized Peer-to-Peer Energy Trading in Community of Flexible Microgrids

This article proposes a novel platform for microgrid (MG) prosumers that can actively trade energy with the power grid and each other directly. This platform provides Peer-to-Peer (P2P) energy trading among MG prosumers to achieve a win–win outcome in the presence of emerging energy resources, such as electric vehicles (EVs), energy storage systems (ESSs), and demand response programs (DRPs). P2P energy trading, from the power system perspective, can facilitate energy balance locally and self-sufficiency. Despite the conventional noncooperative game that players act individually, prosumers can cooperate in exchanging energy and reaping economic benefits in the proposed model. To this end, a bargaining cooperative game is adopted due to MGs autonomy and self-interest. Besides, to avoid prosumers’ private data launching, the fast-alternating direction method of multipliers is introduced to solve MGs' energy management problem in a decentralized manner. A robust optimization method is also applied to manage electricity market uncertainty, allowing MGs operators to decide how much risk they want to consider by adjusting the uncertainty budget parameter. The numerical results show that MGs can actively trade with each other and achieve economic benefits. Moreover, many of the utilized technologies such as ESS, DRP, and EVs assist MGs in sharing more energy with each other.

Optimal decentralized coordinated operation of electric vehicle aggregators enabling vehicle to grid option using distributed algorithm

Electric vehicle (EV) aggregators play the role of intermediate entities between electric vehicles and the grid who can work independently or as the grid operator's agents within the electric network. For all the benefits they can provide through collaboration with other entities like the grid operator and distributed generator (DG), the uncoordinated action of EV aggregators can bring about undesired consequences such as high losses, voltage deviation, peak demand escalation and hence a huge inefficiency of the network operation. In this paper, a unique decentralized approach for the coordination of independent privately-owned EV aggregators and distributed generators is proposed. In this framework, the objective functions representing the goals of the aggregators and generators seek higher profits or lower costs. The objectives also take account of the distribution system operator (DSO) requirements encompassing technical indices such as losses and bus voltages. Several EV-related uncertainties including the plug-in/ plug-out times, the initial state of charge as well as the variations in the number of aggregators and distributed generators, techno-economical parameters of the grid such as the price and load variations and the conflicts of interest among the three parties contribute to the model complexity. For this purpose, a decentralized method based on the Fast Alternating Direction Method of Multipliers (FADMM) is employed to solve the model. The proposed approach is tested on two 33-bus and 69-bus distribution test networks comprised of aggregators and DGs through different scenarios. The results demonstrate that, while retaining the privacy of different agents, the proposed algorithm guarantees the objectives of both aggregators and DGs through higher profits and in the meantime ensures the technical fulfillment for the grid operator. Finally, the effect of varying parameters on the personal and mutual objectives of the mentioned players is evaluated.

Aggregated operation of heterogeneous small-capacity distributed energy resources in peer-to-peer energy trading

Distributed energy resources (DERs) can provide flexibility and promote controllability for distribution networks. However, there are still some obstacles in the management of the small-capacity DERs. In this paper, an aggregated operation model of various heterogeneous DERs in peer-to-peer (P2P) energy trading is proposed. First, a supervised-learning assisted aggregation model of DERs is presented, which aims at estimating the aggregated parameters of heterogeneous DERs. Second, a P2P trading model is proposed for the aggregated DERs. The aggregators can trade with each other in a distributed manner so that privacy can be protected. Third, the fast alternating direction method of multipliers (F-ADMM) is utilized to accelerate the iteration process between the aggregators. Therefore, a quick decision can be made, and less information exchange is required between aggregators, which can reduce the communication burden. The effectiveness of the proposed methodology is verified in case studies.

Designing a Robust Decentralized Energy Transactions Framework for Active Prosumers in Peer-to-Peer Local Electricity Markets

In this paper, a fully decentralized local energy market based on peer-to-peer(P2P) trading is proposed for small-scale prosumers. In the proposed market, the prosumers are classified as buyers and sellers and can bilaterally engage in energy trading (P2P) with each other. The buyer prosumers are equipped with electrical storage and can participate in a demand response (DR) program while protecting their privacy. In addition to bilateral negotiating with the local sellers, these players can compensate for their energy deficiency from the upstream market as the retail market at hours without local generation. In this paper, the retail market price is assumed uncertain. Robust optimization is applied to model this uncertainty in the buyer prosumers model. The proposed decentralized robust optimization guarantees the solution’s existence for each realization of uncertainty components. Furthermore, it performs optimization to realize the hard worse case from uncertainty components. A fully decentralized approach known as the fast alternating direction method of multipliers (FADMM) is employed to solve the proposed decentralized robust problem. The proposed approach does not require third-party involvement as a supervisory node nor disclose the players’ private information. Numerical studies were carried out on a small distribution system with several prosumers. The numerical results suggested the operationality and applicability of the proposed decentralized robust framework and the decentralized solving method.

Peer-to-Peer Energy Trading in Transactive Markets Considering Physical Network Constraints

In recent years, the rapid growth of active consumers in the distribution networks transforms the modern power markets' structure more independent, flexible, and distributed. Specifically, in the recent trend of peer-to-peer (P2P) transactive energy systems, the traditional consumers became prosumers (producer+consumer) who can maximize their energy utilization by sharing it with neighbors without any conventional arbitrator in the transactions. Although a distributed energy pricing scheme is inevitable in such systems to make optimal decisions, it is challenging to establish under the influence of non-linear physical network constraints with limited information. Therefore, this paper presents a distributed pricing strategy for P2P transactive energy systems considering voltage and line congestion management, which can be utilized in various power network topologies. This paper also introduces a new mutual reputation index as a product differentiation between the prosumers to consider their bilateral trading willingness. In this paper, a Fast Alternating Direction Method of Multipliers (F-ADMM) algorithm is realized instead of the standard ADMM algorithm to improve the convergence rate. The effectiveness of the proposed approach is validated through software simulations. The result shows that the algorithm is scalable, converges faster, facilitates easy implementation, and ensures maximum social welfare/profit.

Computationally Efficient Sparse Aperture ISAR Autofocusing and Imaging Based on Fast ADMM

In the case of sparse aperture, the coherence between pulses of radar echo is destroyed, which challenges inverse synthetic aperture radar (ISAR) autofocusing and imaging. Mathematically, reconstructing the ISAR image from the sparse aperture radar echo is a linear underdetermined inverse problem, which, by nature, can be solved by the fast developed compressive sensing (CS) or sparse signal recovery theory. However, the CS-based sparse aperture ISAR imaging algorithms are generally computationally heavy, which becomes the bottleneck of preventing their applications to the real-time ISAR imaging system. In this article, we propose a novel and computationally efficient ISAR autofocusing and imaging algorithm for sparse aperture. We first consider a generalized CS model for ISAR imaging and autofocusing with sparse and entropy-minimization regularizations, and then utilize the alternating direction method of multipliers (ADMM) algorithm to optimize the model. To improve computational efficiency, the matrix inversion is translated to an elementwise division with the usage of a partial Fourier dictionary, and the 2-D ISAR image is updated as a whole instead of range cellwise. To achieve autofocusing for sparse aperture, the phase error is estimated by minimizing the entropy of the ISAR image reconstructed in each iterative loop. Experiments based on both simulated and measured data validate that the proposed algorithm can achieve well-focused ISAR images within a few seconds, which is ten times faster than the reported sparse aperture ISAR imaging algorithms.

Fast ADMM for homogeneous self-dual embedding of sparse SDPs

We propose an efficient first-order method, based on the alternating direction method of multipliers (ADMM), to solve the homogeneous self-dual embedding problem for a primal-dual pair of semidefinite programs (SDPs) with chordal sparsity. Using a series of block eliminations, the per-iteration cost of our method is the same as applying a splitting method to the primal or dual alone. Moreover, our approach is more efficient than other first-order methods for generic sparse conic programs since we work with smaller semidefinite cones. In contrast to previous first-order methods that exploit chordal sparsity, our algorithm returns both primal and dual solutions when available, and a certificate of infeasibility otherwise. Our techniques are implemented in the open-source MATLAB solver CDCS. Numerical experiments on three sets of benchmark problems from the library SDPLIB show speed-ups compared to some common state-of-the-art software packages.

Fast ADMM for Distributed Model Predictive Control of Cooperative Waterborne AGVs

This brief proposes a distributed predictive path following controller with arrival time awareness for multiple waterborne automated guided vessels (waterborne AGVs) applied to interterminal transport (ITT). The goal is to design an efficient cooperative distributed algorithm that solves local problems in parallel and minimizes an overall objective. We model the ITT problem using waterborne AGVs with independent dynamics and objectives but coupling collision avoidance constraints. The problem is then solved by distributed model predictive control (DMPC) of which the parallelism is realized using the alternating direction method of multipliers (ADMM). Successive linearizations are utilized to maintain a tradeoff among computational complexity, optimality, and ease of decomposition. Moreover, we propose a fast ADMM by iteratively incorporating in local problems adaptive global information to improve convergence rates. Simulation results for an ITT case study illustrate the effectiveness of the proposed algorithms for DMPC of time-varying networks in general and cooperative distributed waterborne AGVs in particular.

Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes.

Recently, regression analysis has become a popular tool for face recognition. Most existing regression methods use the one-dimensional, pixel-based error model, which characterizes the representation error individually, pixel by pixel, and thus neglects the two-dimensional structure of the error image. We observe that occlusion and illumination changes generally lead, approximately, to a low-rank error image. In order to make use of this low-rank structural information, this paper presents a two-dimensional image-matrix-based error model, namely, nuclear norm based matrix regression (NMR), for face representation and classification. NMR uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the regression coefficients. We further develop a fast ADMM algorithm to solve the approximate NMR model and show it has a quadratic rate of convergence. We experiment using five popular face image databases: the Extended Yale B, AR, EURECOM, Multi-PIE and FRGC. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression-based methods for face recognition in the presence of occlusion and illumination variations.

Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty

We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of convergence by automatically deciding the constraint penalty needed for parameter consensus in each iteration. In addition, we also propose an extension of the method that adaptively determines the maximum number of iterations to update the penalty. We show that this approach effectively leads to an adaptive, dynamic network topology underlying the distributed optimization. The utility of the new penalty update schemes is demonstrated on both synthetic and real data, including an instance of the probabilistic matrix factorization task known as the structure from motion problem.

Fast linearized alternating direction method of multipliers for the augmented $$\ell _1$$ ℓ 1 -regularized problem

The problem of reconstructing a sparse signal from an underdetermined linear system captures many applications. And it has been shown that this NP-hard problem can be well approached via heuristically solving a convex relaxation problem where the $$\ell _1 $$ -norm is used to induce sparse structure. However, this convex relaxation problem is nonsmooth and thus not tractable in general, besides, this problem has a lower convergence rate. For these reasons, a signal reconstruction algorithm for solving the augmented $$\ell _1$$ -regularized problem is proposed in this paper. The separable structure of the new model enables us to solve the involved subproblems more efficiently by splitting the augmented Lagrangian function. Hence, an implementable numerical algorithm which called fast linearized alternating direction method of multipliers (FLADMM) is proposed to solve this novel model. Our experimental results show that the FLADMM method yields a higher peak signal-to-noise ratio reconstructed signal as well as a faster convergence rate at the same sampling rate as compared to the linearized Bregman method (LBM), the fast linearized Bregman iteration (FLBI) algorithm and the fast alternating direction method of multipliers (FADMM). Besides, this method is more robust than the LBM, FLBI and the FADMM algorithms at the same noise level.