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We consider transmission over the ergodic fading multiple-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent non-fading channel, capacity has recently been shown to be achievable using transmission schemes that were designed for the "dirty paper" channel. We focus on a similar "fading paper" model. The evaluation of the fading paper capacity is difficult to obtain. We confine ourselves to the linear-assignment capacity, which we define, and use convex analysis methods to prove that its maximizing distribution is Gaussian. We compare our fading-paper transmission to an application of dirty paper coding that ignores the partial state information and assumes the channel is fixed at the average fade. We show that a gain is easily achieved by appropriately exploiting the information. We also consider a cooperative upper bound on the sum-rate capacity as suggested by Sato. We present a numeric example that indicates that our scheme is capable of realizing much of this upper bound. [ABSTRACT FROM AUTHOR]

In this paper, we design two efficient quadrature amplitude modulation (QAM) signal detectors for massive multiple-input multiple-output (MIMO) communication systems via the penalty-sharing alternating direction method of multipliers (PS-ADMM). The content of the paper is summarized as follows: first, we transform the maximum-likelihood detection model to a non-convex sharing optimization problem for massive MIMO-QAM systems, where a high-order QAM constellation is decomposed to a sum of multiple binary variables, integer constraints are relaxed to box constraints, and quadratic penalty functions are added to the objective function to result in a favorable integer solution; second, a customized ADMM algorithm, called PS-ADMM, is presented to solve the formulated non-convex optimization problem. In the implementation, all variables in each vector can be solved analytically and in parallel; and third, in order to solve the penalty-sharing distributively, we improve the proposed PS-ADMM algorithm to a distributed one, named DPS-ADMM. In the end, performance analyses of the proposed two algorithms, including convergence properties and computational cost, are provided. Simulation results demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a novel distributed approach to solve a new dynamic economic dispatch problem (DEDP) in which environmental cost function and ramp rate constraints are taken into consideration in islanded microgrid. In our proposed optimization model, the environmental cost function with E-exponential term and ramp rate constraints are considered to make the optimization problem more practical. Then a novel fully distributed algorithm is proposed to address the DEDP based on the alternating direction method of multipliers (ADMM) and distributed consensus theory of the multiagents system. A Lambert $W$ function is employed to tackle the E-exponential term in the environmental cost function, which is different from most existing papers which discuss the DEDP only with quadratic cost functions. A parallel projection method on account of ADMM is used to deal with the ramp rate constraints in this paper. In addition, the power balance can be guaranteed every time when the sum of initial powder output is equal to the total demand. Therefore, the proposed algorithm can deal with the supply-demand constraints, capacity limit constraints, and ramp rate constraints. Finally, simulations on IEEE14-bus are introduced to further illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed adaptive robust voltage/var control (DAR-VVC) method in active distribution networks to minimize power loss while keeping operating constraints under uncertainties. The DAR-VVC aims to coordinate on-load tap changers, capacitor banks and PV inverters in multiple operation stages through a distributed algorithm. To improve efficiency of the distributed algorithm, an affinity propagation clustering algorithm is employed to divide the distribution network by aggregating “the close nodes” together and setting “the far nodes” apart, leading to the network partition where the information exchange between adjacent sub-networks is reduced. Moreover, the virtual load which describes load characteristics of the sub-networks is applied to enhance the boundary conditions. To fully deal with the uncertainties, the proposed DAR-VVC is formulated in a robust optimization model which considers the worst case to guarantee solution robustness against uncertainty realization. Besides, this paper develops an alternating optimization procedure integrating a column-and-constraint generation algorithm and an alternating direction method of multipliers to solve the DAR-VVC problem. The proposed approach is tested on IEEE 33 and IEEE 123 bus distribution test system and numerical simulations verify high efficiency and full solution robustness of the DAR-VVC. [ABSTRACT FROM AUTHOR]

Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a more general set of convex programs known as semi-definite and second-order cone programs. However, these methods are excessively slow for high dimensions. On the other hand, optimization algorithms on manifolds have shown great abilities in finding solutions to non-convex problems in a reasonable time. This paper suggests using a Riemannian optimization approach to solve a subset of convex optimization problems wherein the optimization variable is a doubly stochastic matrix. Optimization over the set of doubly stochastic matrices is crucial for multiple communications and signal processing applications, especially graph-based clustering. The paper introduces and investigates the geometries of three convex manifolds, namely the doubly stochastic, the symmetric, and the definite multinomial manifolds which generalize the simplex, also known as the multinomial manifold. Theoretical complexity analysis and numerical simulation results testify the efficiency of the proposed method over state-of-the-art algorithms. In particular, they reveal that the proposed framework outperforms conventional generic and specialized approaches, especially in high dimensions. [ABSTRACT FROM AUTHOR]

A novel real-time distributed market framework at the distribution grid level is proposed in this paper. The framework coordinates information in a hierarchical manner, while aiming to achieve consensus by sharing physically coupled information among multiple regional operators. In principle, each region maximizes its individual social-welfare problem, which is the local (regional) version of the overall social-welfare maximization of the distribution grid. The individual problem incorporates the coupled physical information from its neighboring regions. The consensus among all regions is then enforced through the proposed consensus-alternating direction method of multipliers structured trust-region (CAST) algorithm. Upon achieving convergence, the distribution locational marginal price (DLMP) is recovered for each region, which is novel in a sense that on the one hand, it is computed in a distributed manner, i.e., with preserving local information, and on the other hand, it accurately represents loss allocation from its neighboring regions. The proposed methodologies are tested on an IEEE 33-bus distribution grid and on a 144-bus network with five regions. [ABSTRACT FROM AUTHOR]

Rooftop solar and batteries, along with other distributed energy resources (DERs), add a new demand-side flexibility, which, when harnessed, will enable distribution operators to more efficiently manage their constrained networks. This paper presents network-aware coordination (NAC), an approach for coordinating DER within unbalanced distribution network constraints, which utilizes the alternating direction method of multipliers (ADMMs) to solve a distributed receding-horizon OPF. As far as we are aware, this paper is the first to report on the practical implementation and performance of an ADMM-based technique solving a significant network problem in live operations. We present real-world trial results of NAC coordinating 31 residential batteries on a constrained feeder within Tasmania’s 11-kV distribution network. The batteries are coordinated to manage the network’s constraints during periods of high feeder demand, decreasing the need for expensive conventional network management, in this case a diesel generator. We achieve a 34% reduction in diesel over seven peaks with 31 batteries capable of meeting 10% of peak demand. Supplementary simulations indicate the potential for a 74% diesel reduction if battery numbers were increased to 100. We find that compared to uncoordinated battery response, the NAC achieves 13% lower total costs over the trial period. [ABSTRACT FROM AUTHOR]

The integration of condition monitoring with queueing systems to support decision making is not well explored. This paper addresses the impact of condition monitoring of the server on the system-level performance experienced by entities in a queueing system. The system consists of a queue with a single-server subject to Markovian degradation. The model assumes a Poisson arrival process with service times and repair times according to general distributions. We develop stability conditions and perform steady-state analysis to obtain performance measures (average queue length, average degradation, and so on). We propose minimizing an objective function involving four types of costs: repair, catastrophic failure, quality, and holding. The queue performance measures derived from steady-state analysis are benchmarked and compared to those from a discrete event simulation model. After verifying the queuing model, a sensitivity analysis is performed to determine the relationships between system performance and model parameters. Results indicate that the total cost function is convex and, thus, subject to an optimal repair policy. The model is sensitive to service time, quality costs, and failure costs for late-stage policy repairs decisions and sensitive to expected repair times and repair costs for early stage policy repair decisions. Note to Practitioners—We propose condition-based maintenance for queues with degrading servers. The proposed model has been verified in simulation using degradation data of tools in a manufacturing facility. In order to implement, one must first model the underlying degradation process using the data from condition monitoring. We can get service and repair time distributions using data from the plant floor. Then, we need reasonable estimates of costs. These include costs of holding, quality, repair, and failure. They can be relative, prioritized or zero. The long-run average cost per unit time can then be evaluated. Then, the model provides the degradation state of the server at which maintenance is the most cost efficient. The degradation data can be used to continually obtain the optimal state of degradation at which the server can be taken offline with minimal costs. [ABSTRACT FROM AUTHOR]

This paper presents novel numerical approaches to finding the secrecy capacity of the multiple-input multiple-output (MIMO) wiretap channel subject to multiple linear transmit covariance constraints, including sum power constraint, per antenna power constraints and interference power constraint. An analytical solution to this problem is not known and existing numerical solutions suffer from slow convergence rate and/or high per-iteration complexity. Deriving computationally efficient solutions to the secrecy capacity problem is challenging since the secrecy rate is expressed as a difference of convex functions (DC) of the transmit covariance matrix, for which its convexity is only known for some special cases. In this paper we propose two low-complexity methods to compute the secrecy capacity along with a convex reformulation for degraded channels. In the first method we capitalize on the accelerated DC algorithm which requires solving a sequence of convex subproblems, for which we propose an efficient iterative algorithm where each iteration admits a closed-form solution. In the second method, we rely on the concave-convex equivalent reformulation of the secrecy capacity problem which allows us to derive the so-called partial best response algorithm to obtain an optimal solution. Notably, each iteration of the second method can also be done in closed form. The simulation results demonstrate a faster convergence rate of our methods compared to other known solutions. We carry out extensive numerical experiments to evaluate the impact of various parameters on the achieved secrecy capacity. [ABSTRACT FROM AUTHOR]

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the $\varepsilon $ -constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method. [ABSTRACT FROM PUBLISHER]

Variance reduction is popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both euclidean space and Riemannian manifold. This paper further improves on existing variance reduction methods for non-convex Riemannian optimization, including R-SVRG and R-SRG/R-SPIDER by providing a unified framework for batch size adaptation. Such framework is more general than the existing works by considering retraction and vector transport and mini-batch stochastic gradients. We show that the adaptive-batch variance reduction methods require lower gradient complexities for both general non-convex and gradient dominated functions, under both finite-sum and online optimization settings. Moreover, under the new framework, we complete the analysis of R-SVRG and R-SRG, which is currently missing in the literature. We prove convergence of R-SVRG with much simpler analysis, which leads to curvature-free complexity bounds. We also show improved results for R-SRG under double-loop convergence, which match the optimal complexities as the R-SPIDER. In addition, we prove the first online complexity results for R-SVRG and R-SRG. Lastly, we discuss the potential of adapting batch size for non-smooth, constrained and second-order Riemannian optimizers. Extensive experiments on a variety of applications support the analysis and claims in the paper. [ABSTRACT FROM AUTHOR]

Future distribution grids are expected to face an increasing penetration of electric vehicles (EVs) and heterogeneous distributed energy resources (DERs). This demands a distributed energy management (EM) to manage power generation and delivery of energy sources to maintain power quality under the impact of EV charging, to save operating costs, and to enhance resiliency. However, the global optimality of the distributed EM’s optimization problem is still an issue in existing works because of the non-convex nature of the optimization problem. In this paper, a distributed EM strategy for grid-connected distribution networks is proposed. In particular, the EM strategy is composed of two steps. In the first step, some conditions of the EM optimization task are relaxed to apply an algorithm converging to the global optimality. The results of the first step are used to reconfigure constraints of the full optimization problem in Step 2. The proposed scheme is validated by implementing the real-time controller-hardware-in-the-loop (CHIL) experimentation on the IEEE 33 bus system. To study the impact of EV charging, EV data is collected from the market and the literature to generate realistic EV load profiles to demonstrate the effectiveness of the proposed strategy on saving operating costs and maintaining power quality. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming procedures are used to solve this problem. This paper is devoted to presenting theoretical explanations for these phenomena by employing some basic tools from Gaussian process theory. Specifically, we identify the precise locations of the phase transitions for both constrained and penalized recovery procedures. Our theoretical results show that these phase transitions are determined by some geometric measures of structure, e.g., the spherical Gaussian width of a tangent cone and the Gaussian (squared) distance to a scaled subdifferential. By utilizing the established phase transition theory, we further investigate the relationship between these two kinds of recovery procedures, which also reveals an optimal strategy (in the sense of Lagrange theory) for choosing the tradeoff parameter in the penalized recovery procedure. Numerical experiments are provided to verify our theoretical results. [ABSTRACT FROM AUTHOR]

Different from the existing works that focus on transceiver design of over-the-air computation (AirComp) over static networks, we in this paper consider an unmanned aerial vehicle (UAV) aided AirComp system, where the UAV as a flying base station aggregates data from mobile sensors. The trajectory design of the UAV provides an additional degree of freedom to improve the performance of AirComp. We aim to minimize the time-averaged mean-squared error (MSE) of AirComp by jointly optimizing the UAV trajectory, receive normalizing factors, and sensors’ transmit power. To this end, we first propose a novel and equivalent problem transformation by introducing intermediate variables. This reformulation leads to a convex subproblem when fixing any other two blocks of variables, thereby enabling efficient algorithm design based on the principle of block coordinate descent and alternating direction method of multipliers (ADMM) techniques. In particular, we derive the optimal closed-form solutions for normalizing factors and intermediate variables optimization subproblems. We also recast the convex trajectory design subproblem into an ADMM form and obtain the closed-form expressions for each variable updating. Simulation results show that the proposed algorithm achieves a smaller time-averaged MSE while reducing the simulation time by orders of magnitude compared to state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector $\ell _1$ ℓ 1 norm, which is given by the soft-thresholding operator. In this paper we study the proximal operator of the mixed $\ell _{1,\infty }$ ℓ 1 , ∞ matrix norm and show that it can be computed in closed form by applying the well-known soft-thresholding operator to each column of the matrix. However, unlike the vector $\ell _1$ ℓ 1 norm case where the threshold is constant, in the mixed $\ell _{1,\infty }$ ℓ 1 , ∞ norm case each column of the matrix might require a different threshold and all thresholds depend on the given matrix. We propose a general iterative algorithm for computing these thresholds, as well as two efficient implementations that further exploit easy to compute lower bounds for the mixed norm of the optimal solution. Experiments on large-scale synthetic and real data indicate that the proposed methods can be orders of magnitude faster than state-of-the-art methods. [ABSTRACT FROM AUTHOR]

We consider an $\ell _{2}$ -regularized non-convex optimization problem for recovering signals from their noisy phaseless observations. We design and study the performance of a message passing algorithm that aims to solve this optimization problem. We consider the asymptotic setting $m,n \rightarrow \infty $ , $m/n \rightarrow \delta $ and obtain sharp performance bounds, where $m$ is the number of measurements and $n$ is the signal dimension. We show that for complex signals, the algorithm can perform accurate recovery with only $m = (({64}/{\pi ^{2}})-4)n \approx 2.5n$ measurements. Also, we provide a sharp analysis on the sensitivity of the algorithm to noise. We highlight the following facts about our message passing algorithm: 1) adding $\ell _{2}$ regularization to the non-convex loss function can be beneficial and 2) spectral initialization has a marginal impact on the performance of the algorithm. The sharp analyses, in this paper, not only enable us to compare the performance of our method with other phase recovery schemes but also shed light on designing better iterative algorithms for other non-convex optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, we devise a communication-efficient decentralized algorithm, named as communication-censored alternating direction method of multipliers (ADMM) (COCA), to solve a convex consensus optimization problem defined over a network. Similar to popular decentralized consensus optimization algorithms such as ADMM, at every iteration of COCA, a node exchanges its local variable with neighbors, and then updates its local variable according to the received neighboring variables and its local cost function. A different feature of COCA is that a node is not allowed to transmit its local variable to neighbors, if this variable is not sufficiently different to the previously transmitted one. The sufficiency of the difference is evaluated by a properly designed censoring function. Though this censoring strategy may slow down the optimization process, it effectively reduces the communication cost. We prove that when the censoring function is properly chosen, COCA converges to an optimal solution of the convex consensus optimization problem. Furthermore, if the local cost functions are strongly convex, COCA has a fast linear convergence rate. Numerical experiments demonstrate that, given a target solution accuracy, COCA is able to significantly reduce the overall communication cost compared to existing algorithms including ADMM, and hence fits for applications where network communication is a bottleneck. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of maximizing the minimum power gain in a wide main lobe for an array antenna. To obtain the desired power gain pattern, current literatures solve the problem known as shaped beam pattern synthesis (SBPS) by setting the beam pattern expression as the cost function. The power gain in a certain direction of the array antenna is comprehensively decided by the array radiated power density and the total radiated power. Both these two parameters are affected by the selection of array elements’ weights. However, the SBPS-based methods do not take the total radiated power into account. Therefore, the SBPS-based methods cannot obtain the power gain pattern directly, and the optimal power gain pattern, consequently, cannot be guaranteed. To overcome this deficiency, this paper maximizes the minimum power gain in the desired wide main lobe by directly setting the power gain expression as the cost function. Aiming at optimizing the cost function, this paper first sets up a power gain optimization problem which has concave form. Termed this optimization problem as the power gain pattern synthesis (PGPS) problem. The concave PGPS problem is then converted to a series of convex subproblems and an iterative algorithm is proposed to solve it efficiently. Solution to the PGPS problem is proven to be able to achieve higher minimum power gain in a desired wide main lobe than the results from the SBPS-based algorithms. Simulations are carried out with both linear array antenna and planar array antenna. Comparisons with the existed SBPS-based algorithms validate the effectiveness and advantages of the proposed PGPS-based algorithm. In addition, further improvement on suppressing the sidelobe level for the PGPS problem is discussed. [ABSTRACT FROM AUTHOR]

Deep unfolding network (DUN) has become the mainstream for compressive sensing MRI (CS-MRI) due to its good interpretability and high performance. Different optimization algorithms are usually unfolded into deep networks with different architectures, in which one iteration corresponds to one stage of DUN. However, there are few works discussing the following two questions: Which optimization algorithm is better after being unfolded into a DUN? What are the bottlenecks in existing DUNs? This paper attempts to answer these questions and give a feasible solution. For the first question, our mathematical and empirical analysis verifies the similarity of DUNs unfolded by alternating minimization (AM), alternating iterative shrinkage-thresholding algorithm (ISTA) and alternating direction method of multipliers (ADMM). For the second question, we point out that one major bottleneck of existing DUNs is that the input and output of each stage are just images of one channel, which greatly limits the transmission of network information. To break the information bottleneck, this paper proposes a novel, simple yet powerful high-throughput deep unfolding network (HiTDUN), which is not constrained by any optimization algorithm and can transmit multi-channel information between adjacent network stages. The developed multi-channel fusion strategy can also be easily incorporated into existing DUNs to further boost their performance. Extensive CS-MRI experiments on three benchmark datasets demonstrate that the proposed HiTDUN outperforms existing state-of-the-art DUNs by large margins while maintaining fast computational speed. 1 For reproducible research, the source codes and training models of our HiTDUN. [Online]. Available: https://github.com/jianzhangcs/HiTDUN. [ABSTRACT FROM AUTHOR]

This paper focuses on the distributionally robust dispatch for integrated transmission-distribution (ITD) systems via distributed optimization. Existing distributed algorithms usually require synchronization of all subproblems, which could be hard to scale, resulting in the under-utilization of computation resources due to the subsystem heterogeneity in ITD systems. Moreover, the most commonly used distributionally robust individual chance-constrained dispatch models cannot systematically and robustly ensure simultaneous security constraint satisfaction. To address these limitations, this paper presents a novel distributionally robust joint chance-constrained (DRJCC) dispatch model for ITD systems via asynchronous decentralized optimization. Using the Wasserstein-metric based ambiguity set, we propose data-driven DRJCC models for transmission and distribution systems, respectively. Furthermore, a combined Bonferroni and conditional value-at-risk approximation for the joint chance constraints is adopted to transform the DRJCC model into a tractable conic formulation. Meanwhile, considering the different grid scales and complexity of subsystems, a tailored asynchronous alternating direction method of multipliers (ADMM) algorithm that better adapts to the star topological ITD systems is proposed. This asynchronous scheme only requires local communications and allows each subsystem operator to perform local updates with information from a subset of, but not all, neighbors. Numerical results illustrate the effectiveness and scalability of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, an uplink non-orthogonal multiple access (NOMA) terrestrial-satellite network is investigated, where the terrestrial base stations (BSs) communicate with satellite by backhaul link, and user equipments (UEs) share spectrum resource of access link. Firstly, a utility function which consists of the achieved terrestrial user rate and cross-tier interference caused by terrestrial BSs to satellite is design. Thus, the optimization problem can be modeled by maximizing the system utility function while satisfying the varying backhaul rate and UEs’ quality of service (QoS) constraints. The optimization problem is highly non-convex and can not be solved directly. Thus, we decouple the original problem into user association sub-problem, bandwidth assignment sub-problem, and power allocation sub-problem. In user association sub-problem, an enhanced-caching, preference relation, and swapping based algorithm is proposed, where the satellite UEs are selected by the channel coefficient ratio. The terrestrial UEs association considers the both caching state and backhaul link. Then we derive the closed-form expression of the bandwidth assignment. In power allocation sub-problem, we convert the non-convex term of the target function into the convex one by the Taylor expansion, and solve the transformed convex problem by an iterative power allocation algorithm. Finally, a three-stages iterative resource allocation algorithm by joint considering the three sub-problems is proposed. Simulation results are discussed to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with two typical random number generation problems in information theory. One is the source resolvability problem (resolvability problem for short) and the other is the intrinsic randomness problem. In the literature, optimum achievable rates in these two problems with respect to the variational distance as well as the Kullback-Leibler (KL) divergence have already been analyzed. On the other hand, in this study we consider these two problems with respect to $f$ -divergences. The $f$ -divergence is a general non-negative measure between two probabilistic distributions on the basis of a convex function $f$. The class of $f$ -divergences includes several important measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence, it is meaningful to consider the random number generation problems with respect to $f$ -divergences. In this paper, we impose some conditions on the function $f$ so as to simplify the analysis, that is, we consider a subclass of $f$ -divergences. Then, we first derive general formulas of the first-order optimum achievable rates with respect to $f$ -divergences. Next, we particularize our general formulas to several specified functions $f$. As a result, we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas. The second-order optimum achievable rates and optimistic optimum achievable rates have also been investigated. [ABSTRACT FROM AUTHOR]

This paper studies the uplink of a cloud radio access network (C-RAN) where the cell sites are connected to a cloud-computing-based central processor (CP) with noiseless backhaul links with finite capacities. We employ a simple compress-and-forward scheme in which the base stations (BSs) quantize the received signals and send the quantized signals to the CP using either distributed Wyner–Ziv coding or single-user compression. The CP first decodes the quantization codewords and then decodes the user messages as if the remote users and the cloud center form a virtual multiple-access channel (VMAC). This paper formulates the problem of optimizing the quantization noise levels for weighted sum rate maximization under a sum backhaul capacity constraint. We propose an alternating convex optimization approach to find a local optimum solution to the problem efficiently, and more importantly, to establish that setting the quantization noise levels to be proportional to the background noise levels is near optimal for sum-rate maximization when the signal-to-quantization-noise-ratio (SQNR) is high. In addition, with Wyner–Ziv coding, the approximate quantization noise level is shown to achieve the sum-capacity of the uplink C-RAN model to within a constant gap. With single-user compression, a similar constant-gap result is obtained under a diagonal dominant channel condition. These results lead to an efficient algorithm for allocating the backhaul capacities in C-RAN. The performance of the proposed scheme is evaluated for practical multicell and heterogeneous networks. It is shown that multicell processing with optimized quantization noise levels across the BSs can significantly improve the performance of wireless cellular networks. [ABSTRACT FROM PUBLISHER]

Alternating direction method of multipliers (ADMM) is a widely used tool for machine learning in distri-buted settings where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to analyze the end-to-end privacy loss. The theoretical analysis shows that the DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates a novel near-optimal finite-control-set model predictive control (NOP-MPC) algorithm to control the grid-connected, pulsewidth-modulator-driven voltage source converters with LCL filters. Exploiting the convex and elliptical paraboloid properties of the cost error, NOP-MPC adopts a systematic iterative algorithm within each control cycle to progressively synthesize finite sets of virtual voltage vectors (VVs) for the control optimization stage. The synthesis has the inherent features of respecting the converter voltage limits and converging the sets of VV candidates toward the global optimal point. The fixed-switching-frequency feature of NOP-MPC is expected to ease the LCL filter design. Effects of computational delay, pulsewidth modulation delay, and deadtime are considered and compensated successfully. A two-vector-variable cost function is used to actively damp the inherent LC resonance through an adjustable, weighting-factor-based damping level. This paper is substantiated by theoretical consideration, simulation and experimental results, parameter sensitivity study, and a comparative study with the standard finite-control-set model predictive control that uses only actual VVs. [ABSTRACT FROM AUTHOR]

The paper focuses on the day-ahead operational planning of a grid-connected local energy community (LEC) consisting of an internal low-voltage network and several prosumers including generation units, battery storage systems, and local loads. In order to preserve, as much as possible, the confidentiality of the features of prosumers’ equipment and the production and load forecasts, the problem is addressed by designing a specific distributed procedure based on the alternating direction method of multipliers (ADMM). The distributed procedure calculates the scheduling of the available energy resources to limit the balancing action of the external grid and allocates the internal network losses to the various power transactions. Results obtained for various case studies are compared with those obtained by a centralized optimization approach. The results confirm that, in the considered LEC framework, each of the prosumers achieves a reduction in costs or increases revenues in case it participates to the LEC with respect to the case in which it can only transact with an external energy provider. [ABSTRACT FROM AUTHOR]

This paper presents a robust statistical approach to distributed power system state estimation (DPSSE) under bad data based on iterative reweight least squares (IRWLS) method and an improved alternating direction method of multipliers (ADMM) framework. In particular, the Hampel’s redescending and the Schweppe–Huber generalized M-estimators (SHGM) are studied for mitigating the adverse effect of outliers with large magnitude. Moreover, a new robust weight smoothing scheme is proposed for improving the numerical stability and convergence speed of the algorithm. The proposed approach is further extended to recursive monitoring of measurement devices and inpainting of missing data by utilizing prior information provided in previous state estimation. The resultant algorithm is solved using the Levenberg–Marquardt (LM) solver, which helps to maintain numerical stability under unexpected adverse situations. Experimental results show that the proposed approach outperforms conventional approaches using the ADMM with L1 outlier detection in state estimation accuracy and convergence speed. Moreover, it maintains numerical stability and good performance under missing data. As state estimation will be performed more frequently in future smart grid due to the increased penetration of renewables, the proposed methods and investigations offer much insight in addressing the missing data and outlier problems in DPSSE. [ABSTRACT FROM AUTHOR]

The reconstruction of the field radiated by a source from square amplitude-only data falls into the realm of phase retrieval. In this paper, we tackle the phase retrieval with two different approaches. The first one is based on a convex optimization problem called PhaseLift. The latter exploits the lifting technique to recast phase retrieval as a linear problem with an increased number of unknowns and then, because the linear problem is highly undetermined, it adds further constraints (based on the mathematical properties of the solution) to estimate it. The second approach formulates phase retrieval as a least squares problem and, therefore, it requires to tackle the minimization of a quartic functional which will be carried out by applying a gradient descent method. In the second part of this paper, in order to corroborate the effectiveness of both approaches, we present the numerical results. Afterward, we provide a comparison between the two methods and finally, we emphasize how the ratio between the number of independent data and the number of unknowns impacts on the performance in both approaches. [ABSTRACT FROM AUTHOR]

Multi-objective optimization of power converters is a time-consuming task, especially when multiple operating points and multiple converter topologies must be considered. As a result, various steps are often taken to simplify the design problem and restrict the size of the design space prior to going through an optimization procedure. While this saves time, it produces potentially sub-optimal designs, and existing approaches must tradeoff between running time and design optimality. This paper presents an optimization-oriented method for modeling power converters and their components as posynomial functions, allowing multi-objective optimization of converters to be formulated as a geometric program, a type of convex optimization problem. This allows the use of fast, powerful solvers that guarantee global optimality of solutions. The method is demonstrated using the example of low-power multi-level flying capacitor step-down converters. Results show that, using geometric programming, sets of globally Pareto-optimal designs of two-, three-, and four-level converters with respect to efficiency and power density, for one design space and one operating point, can be generated in as little as 25 s, on a mid- to upper range laptop computer. Thus, optimal designs for three different converter topologies for hundreds of different operating points and/or design spaces can be generated in several hours—less than the time required to globally optimize one converter topology at one operating point for one design space using currently prevalent methods. This paper also demonstrates how geometric programming can be used to quickly perform sensitivity and tradeoff analysis of optimal converter designs. [ABSTRACT FROM AUTHOR]

This paper presents a practical convex-optimization-based sensorless scheme for interior permanent magnet synchronous motor (IPMSM) drives. The proposed sensorless scheme simplifies the optimization process that employs only one variable as compared with two variables in the existing optimization-based methods. The reduction in variables substantially reduces the computational burden in the proposed scheme and, hence, is suitable for practical applications. Additionally, the proposed algorithm is able to estimate the rotor position regardless of the pattern of the high-frequency (HF) injected signal under low-speed conditions. This characteristic has been investigated in this paper where three typical HF injection patterns are compared. The performance of the proposed scheme is experimentally validated. [ABSTRACT FROM AUTHOR]

In this paper, we present an incremental-oriented alternating direction method of multipliers (ADMM) for distributed optimal power flow with discrete variables in distribution networks. This algorithm consists of outer-loop iterations based on the extended interior-point method (EIPM), and inner-loop iterations based on ADMM. The outer-loop EIPM iteration was used to form a regional linear correction equation with coupling relationships between neighboring areas. This enables us to use ADMM to compute the primal–dual directions in a distributed manner. This novel application of ADMM inside EIPM can be considered as an independent linear equation solver; thus, its convergence can be guaranteed. In particular, the updating of the variable increments can be expressed in a closed form, speeding up ADMM. The resulting algorithm has more attractive convergence properties compared to ADMM directly applied to mixed-integer nonlinear programming problems. The convergence analysis is also given. The test results demonstrated that the proposed algorithm converged reliably and obtained a sufficiently feasible solution. [ABSTRACT FROM AUTHOR]

This paper focuses on precoding design for sum-rate maximization while considering the effects of residual self-interference for multiuser multiple-input–multiple-output (MU-MIMO) full-duplex (FD) systems. The problem formulation leads to a nonconvex matrix-variable optimization problem, where we develop two efficient sum-rate maximization algorithms using sequential convex programming (SCP), namely, the difference of convex functions (DC)-based and the sequential convex approximations for matrix-variable programming (SCAMP) algorithms. In addition, we derive the achievable sum rate under the effect of residual self-interference. Simulation results show that, even in cases of high self-interference and high estimation error, the SCAMP algorithm provides approximately 20%–30% sum-rate improvements over both conventional optimized half-duplex (HD) transmission and the existing state-of-the-art FD algorithm in a wide range of scenarios. Finally, the convergence results indicate that the DC-based algorithm tends to initially give the best performance; however, at convergence, the SCAMP algorithm tends to significantly outperform the other algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a decentralized solution algorithm for network-constrained unit commitment (NCUC) in multiregional power systems. The proposed algorithm is based on our previous work in which a local NCUC was formulated for each control entity (i.e., region) and an analytical target cascading (ATC) based distributed but partially parallelized algorithm requiring a central coordinator was presented. The primary objective of this paper is to present a decentralized approach that relaxes the need for any form of central coordinator in ATC and allows fully parallelized solutions of the local NCUCs. To achieve this objective, we formulate a bilevel optimization problem for each control entity. While the upper level solves the NCUC problem of the control entity, the lower level seeks to coordinate the control entity with its neighboring regions. The lower level is a convex optimization, which can be further replaced in the upper level problem by the Karush–Kuhn–Tucker conditions. The control entities communicate directly with each other and synchronously solve their local NCUCs. Having no need for any form of central coordinator, the proposed algorithm is potentially less vulnerable to cyber-attacks and communication failures than the distributed methods utilizing a coordinator. [ABSTRACT FROM AUTHOR]

Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization, we do not have access directly to such equispaced samples. Rather, we only observe a severely undersampled version of these observations through linear measurements. This paper is about such generalized line spectral estimation problems. We reformulate these problems as sparse signal recovery problems over a continuously indexed dictionary, which can be solved via a convex program. We prove that the frequencies and amplitudes of the components of the mixture can be recovered perfectly from a near-minimal number of observations via this convex program. This result holds provided the frequencies are sufficiently separated, and the linear measurements obey natural conditions that are satisfied in a variety of applications. [ABSTRACT FROM AUTHOR]

In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted l 1 norm, we utilize the l p norm of the array weight vector, where $0

This paper revisit and extend the interesting case of bounds on the $Q$ -factor for a given directivity for a small antenna of arbitrary shape. A higher directivity in a small antenna is closely connected with a narrow impedance bandwidth. The relation between bandwidth and a desired directivity is still not fully understood, not even for small antennas. Initial investigations in this direction have related the radius of a circumscribing sphere to the directivity, and bounds on the $Q$ -factor have also been derived for a partial directivity in a given direction. In this paper, we derive lower bounds on the $Q$ -factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semidefinite relaxation (SDR) techniques. We also show that the relaxed solution is also a solution of the original problem of determining the lower $Q$ -factor bound for a total desired directivity. SDR can also be used to relax a class of other interesting nonconvex constraints in antenna optimization, such as tuning, losses, and front-to-back ratio. We compare two different new methods to determine the lowest $Q$ -factor for arbitrary-shaped antennas for a given total directivity. We also compare our results with full electromagnetic simulations of a parasitic element antenna with high directivity. [ABSTRACT FROM AUTHOR]

Flying platforms, such as unmanned aerial vehicles (UAVs) are a promising solution for future small cell networks. UAVs can be used as aerial base stations (BSs) to enhance coverage, capacity and reliability of wireless networks. Also, with recent advances of self interference cancellation (SIC) techniques in full-duplex (FD) systems, practical implementation of FD BSs is feasible. In this paper, we investigate the problem of resource allocation for multi-small cell networks with FD-UAVs as aerial BSs with imperfect SIC. We consider three different scenarios: a) maximizing the DL sum-rate; b) maximizing the UL sum-rate; and finally c) maximizing the sum of UL and DL sum-rates. The aforementioned problems result in non-convex optimization problems, therefore, successive convex approximation algorithms are developed by leveraging D.C. (Difference of Convex functions) programming to find sub-optimal solutions. Simulation results illustrated validity and effectiveness of the proposed radio resource management algorithms in comparison with ground BSs, in both FD mode and its half-duplex (HD) counterpart. The results also indicate those situations where using aerial BS is advantageous over ground BS and reveal how FD transmission enhances the network performance in comparison with HD one. [ABSTRACT FROM AUTHOR]

Distributed primal-dual methods have been widely used for solving large-scale constrained optimization problems. The majority of existing results focus on the problems with decoupled constraints. Some recent works have studied the problems subject to separable globally coupled constraints. This paper considers the distributed optimization problems with globally coupled constraints over networks without requiring the separability of the globally coupled constraints. This is made possible by the local estimates of the constraint violations. For solving such a problem, we propose a primal-dual algorithm in the augmented Lagrangian framework, combining the average consensus technique. We first establish a non-ergodic convergence rate of $\mathcal {O}(1/k)$ in terms of the objective residual for solving a distributed constrained convex optimization problem, where $k$ is the iteration counter. Specifically, the global objective function is the aggregate of the local convex and possibly non-smooth costs, and the coupled constraint is the sum of the local linear equality constraints. The numerical results illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces a new solution to improve the performance for secondary systems in radio frequency (RF) powered cognitive radio networks (CRNs). In a conventional RF-powered CRN, the secondary system works based on the harvest-then-transmit protocol. That is, the secondary transmitter (ST) harvests energy from primary signals and then uses the harvested energy to transmit data to its secondary receiver (SR). However, with this protocol, the performance of the secondary system is much dependent on the amount of harvested energy as well as the primary channel activity, e.g., idle and busy periods. Recently, ambient backscatter communication has been introduced, which enables the ST to transmit data to the SR by backscattering ambient signals. Therefore, it is potential to be adopted in the RF-powered CRN. We investigate the performance of RF-powered CRNs with ambient backscatter communication over two scenarios, i.e., overlay and underlay CRNs. For each scenario, we formulate and solve the optimization problem to maximize the overall transmission rate of the secondary system. Numerical results show that by incorporating such two techniques, the performance of the secondary system can be improved significantly compared with the case when the ST performs either harvest-then-transmit or ambient backscatter technique. [ABSTRACT FROM AUTHOR]

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called “prosumers,” i.e., proactive consumers, which can both produce and consume power. To encourage energy exchange among prosumers, energy sharing is increasingly adopted, which is usually formulated as a generalized Nash game (GNG). In this paper, a distributed approach is proposed to seek the Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we first prove the strong monotonicity of the game. Then, the GNG is converted into an equivalent optimization problem. An algorithm based on Nesterov's methods is thereby devised to solve the equivalent problem and consequently find the GNE in a distributed manner. The convergence of the proposed algorithm is proved rigorously based on the nonexpansive operator theory. The performance of the algorithm is validated by experiments with three prosumers, and the scalability is tested by simulations using 1888 prosumers. [ABSTRACT FROM AUTHOR]

This paper presents a preconditioned Krasnoselskii-Mann (KM) algorithm with an improved EM preconditioner (IEM-PKMA) for higher-order total variation (HOTV) regularized positron emission tomography (PET) image reconstruction. The PET reconstruction problem can be formulated as a three-term convex optimization model consisting of the Kullback–Leibler (KL) fidelity term, a nonsmooth penalty term, and a nonnegative constraint term which is also nonsmooth. We develop an efficient KM algorithm for solving this optimization problem based on a fixed-point characterization of its solution, with a preconditioner and a momentum technique for accelerating convergence. By combining the EM precondtioner, a thresholding, and a good inexpensive estimate of the solution, we propose an improved EM preconditioner that can not only accelerate convergence but also avoid the reconstructed image being “stuck at zero.” Numerical results in this paper show that the proposed IEM-PKMA outperforms existing state-of-the-art algorithms including, the optimization transfer descent algorithm and the preconditioned L-BFGS-B algorithm for the differentiable smoothed anisotropic total variation regularized model, the preconditioned alternating projection algorithm, and the alternating direction method of multipliers for the nondifferentiable HOTV regularized model. Encouraging initial experiments using clinical data are presented. [ABSTRACT FROM AUTHOR]

In this paper, resource allocation for a multi-carrier uplink non-orthogonal multiple access (NOMA) system is studied. Unlike the existing works on multi-carrier uplink NOMA, in which each user is assumed to access only one subcarrier, we consider a more general scenario where the number of subcarriers allocated to a single user is not constrained. We first aim to maximize the system's sum rate, which requires selecting the appropriate subcarriers for each user and distribute the transmission power. The formulated non-convex problem is transformed into a convex one, and further, an optimal and low-complexity iterative water-filling solution is proposed. Nonetheless, it is shown that maximum transmit power is employed by each user to maximize the sum rate. Motivated by the fact that the users are power constrained, the energy efficiency (EE) maximization problem is also studied. Based on fractional programming, the EE maximization problem is transformed into a series of sum rate maximization subproblems, and the proposed iterative water-filling solution is applied to each subproblem. The proposed schemes are compared with other NOMA-based and orthogonal multiple access based algorithms, and its superiority is fully validated. [ABSTRACT FROM AUTHOR]

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and nonsmooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a previous algorithm, PG-EXTRA (W. Shi, Q. Ling, G. Wu, and W. Yin, “A proximal gradient algorithm for decentralized composite optimization,” IEEE Trans. Signal Process., vol. 63, no. 22, pp. 6013–6023, 2015), but has a few advantages. First of all, agents use uncoordinated step-sizes, and the stable upper bounds on step-sizes are independent of network topologies. The step-sizes depend on local objective functions, and they can be as large as those of the gradient descent. Second, for the special case without nonsmooth terms, linear convergence can be achieved under the strong convexity assumption. The dependence of the convergence rate on the objective functions and the network are separated, and the convergence rate of the new algorithm is as good as one of the two convergence rates that match the typical rates for the general gradient descent and the consensus averaging. We provide numerical experiments to demonstrate the efficacy of the introduced algorithm and validate our theoretical discoveries. [ABSTRACT FROM AUTHOR]

The resilience of modern power systems has been constantly threatened by various natural disasters and man-made attacks. Under those threats, fast and automatic restoration actions are critical for restoring impacted systems to normal operating conditions and preventing from additional disastrous consequences. Smart grid technologies, such as distributed energy resources (DERs) and microgrids, provide both opportunities and challenges for distribution system restoration. In this paper, distributed load restoration (DLR) in unbalanced active distribution networks is developed using the alternating direction method of multipliers (ADMMs) algorithm. The step-by-step restoration actions are provided to schedule the output of DERs and distribution system control devices, as well as the power consumption from transmission system restoration. The nonlinearities from three-phase unbalanced power flow and distribution components modeling are relaxed into a convex quadratic programming model. Then, the problem is decomposed into subproblems for each node by applying ADMM-DLR; and solves through each agent by exchanging limited information with neighboring nodes in an iterative procedure. The developed models and algorithms are validated and demonstrated through testing of the IEEE 13-node and 123-node test feeders. Simulation results demonstrate the effectiveness of restoring unbalanced distribution system with the hybrid bottom-up and top-down restoration strategies. [ABSTRACT FROM AUTHOR]

In this paper, a distributed multi-objective optimization model is proposed to coordinate the fast-dispatch of photovoltaic (PV) inverters with the slow-dispatch of on-load tap changer and capacitor banks for implementing conservation voltage reduction in unbalanced three-phase distribution systems. In existing studies, PV inverters and voltage regulation devices are generally dispatched by fully centralized control frameworks. However, centralized optimization methods are subject to single point of failure and suffer large computational burden. To tackle these challenges, a distributed dispatch method is developed to coordinate PV inverters and conventional voltage regulation devices in distribution systems. The proposed method is based on a modified alternating direction method of multipliers algorithm to handle non-convex optimization problems without relaxing the original formulation, which could lead to sub-optimality. Numerical results from simulations on modified IEEE 13-bus, 34-bus, and 123-bus unbalanced three-phase systems have been used to verify the proposed method. [ABSTRACT FROM AUTHOR]