Block Coordinate Descent Algorithm Research Articles

Energy minimization for IRS-and-UAV-assisted mobile edge computing

Intelligent reconfigurable surface (IRS) is an emerging technology for the enhancement of spectrum and energy efficiency. We propose a novel IRS-and-unmanned aerial vehicle (UAV)-Assisted mobile edge computing (MEC) framework, where a MEC server installing on an UAV to facilitate task calculations by mobile users (MUs), and an IRS modulates channels between MUs and the UAV. Non-orthogonal multiple access (NOMA) is employed for further improving system-wide spectral efficiency. There are needs for joint optimization of multiple parameters, e.g., the task partition parameters and the transmit power of all MUs, the reflection coefficient matrix of the IRS and the movement trajectory of the UAV, and such needs raises the challenge of minimizing the long-term total energy consumption of all MUs while satisfying required transmission rate and task completion delay. We divide optimization tasks into two sub-problems and propose specific solutions respectively, i.e., relevant decisions about the UAV and MUs to be solved by deep reinforcement learning (DRL); and the reflection coefficient matrix of the IRS to be solved by block coordinate descent (BCD). A series of experiments have verified the effectiveness of the proposed communication techniques and optimization algorithms. Simulation results demonstrate that (1) NOMA-IRS technique achieves better energy efficacy compared to the cases where random IRS or no IRS is deployed and the conventional orthogonal multiple access (OMA) technique with IRS. (2) our proposed deep deterministic policy gradient (DDPG)-BCD algorithm outperforms other four benchmark algorithms in solving the complex and dynamic optimization problem.

Tensor-based statistical learning methods for diagnosing product quality defects in multistage manufacturing processes

Multistage manufacturing processes with identical stages provide three-dimensional process data in which the first dimension represents the process (control/sensing) variable, the second is the stage, and the third is the measurement/sampling/data acquisition time point. Diagnosing quality faults in such processes often requires the simultaneous identification of crucial process variables and stages associated with product quality anomalies. Most existing diagnosis methods convert 3D data into a 2D matrix, resulting in loss of information and reduced diagnostic accuracy and stability. To address this challenge, we propose a penalized tensor regression model that regresses the product quality index against its 3D process data. For the estimation of high-dimensional regression coefficients with the limited amount of historical data, we apply the CANDECOMP/PARAFAC and Tucker decompositions to the coefficient tensor, which significantly reduces the number of parameters to be estimated. Based on the decompositions, a new regularization term is designed to enable the joint identification of critical process variables and stages. To estimate the parameters, we develop the block coordinate proximal descent algorithm and provide its convergence guarantee. Numerical studies demonstrate that the proposed methods can enhance diagnostic stability and on average improve the diagnostic accuracy by around 20% over existing benchmarks.

A framework for co-existence of radar and communication with joint design

The integration of both sensing and communication functions is a crucial feature for future communication systems. This paper considers a novel scenario where a radar covers multiple small-cell base stations which operate in different spectra. Due to the limited spectra resource, the radar needs to reuse the spectra of one BS for tracking. To suppress interference and improve performance, we propose a framework including two stages and the corresponding communication and sensing algorithms. Specifically, at the detection stage, we aim to minimize the system transmit power while maintaining the performance of both radar and communication. At the tracking stage, our goal is to maximize the radar sensing performance under a given power budget, while ensuring communication quality. Due to the complexity of the original problem, we address it by introducing auxiliary variables and proposing a penalty dual decomposition-based algorithm, enabling us to solve a more tractable form of the problem. In the inner loop, we propose a concave–convex procedure-based algorithm to handle the optimization problem, while adopting the block coordinate descent algorithm to iteratively update the variables. In the outer loop, we update the penalty term or Lagrange multipliers. Furthermore, we propose a radar target parameter estimation algorithm based on successive interference cancellation, which aims to mitigate communication interference. Finally, numerical simulations demonstrate the effectiveness of the proposed system, and the superior performance of our proposed algorithms over benchmark algorithms.

Jamming precoding in AF relay-aided PLC systems with multiple eavessdroppers

Enhancing information security has become increasingly significant in the digital age. This paper investigates the concept of physical layer security (PLS) within a relay-aided power line communication (PLC) system operating over a multiple-input multiple-output (MIMO) channel based on MK model. Specifically, we examine the transmission of confidential signals between a source and a distant destination while accounting for the presence of multiple eavesdroppers, both colluding and non-colluding. We propose a two-phase jamming scheme that leverages a full-duplex (FD) amplify-and-forward (AF) relay to address this challenge. Our primary objective is to maximize the secrecy rate, which necessitates the optimization of the jamming precoding and transmitting precoding matrices at both the source and the relay while adhering to transmit power constraints. We present a formulation of this problem and demonstrate that it can be efficiently solved using an effective block coordinate descent (BCD) algorithm. Simulation results are conducted to validate the convergence and performance of the proposed algorithm. These findings confirm the effectiveness of our approach. Furthermore, the numerical analysis reveals that our proposed algorithm surpasses traditional schemes that lack jamming to achieve higher secrecy rates. As a result, the proposed algorithm offers the benefit of guaranteeing secure communications in a realistic channel model, even in scenarios involving colluding eavesdroppers.

Faster nonconvex low-rank matrix learning for image low-level and high-level vision: A unified framework

This study introduces a unified approach to tackle challenges in both low-level and high-level vision tasks for image processing. The framework integrates faster nonconvex low-rank matrix computations and continuity techniques to yield efficient and high-quality results. In addressing real-world image complexities like noise, variations, and missing data, the framework exploits the intrinsic low-rank structure of the data and incorporates specific residual measurements. The optimization problem for low-rank matrix learning is effectively solved using the nonconvex Proximal Block Coordinate Descent (PBCD) algorithm, resulting in nearly unbiased estimators. Rigorous theoretical analysis ensures both local and global convergence. The PBCD algorithm updates blocks of variables iteratively with closed-form solutions, adeptly handling nonconvexity and promoting faster convergence. Notably, the framework incorporates the randomized singular value decomposition (RSVD) technique and introduces a continuous strategy for adaptive model parameter updates. These strategic choices reduce computational complexity while maintaining result quality. They offer fine-tuned control over the desired rank of the learned matrix and enhance robustness in a straightforward manner. Furthermore, the versatility of the proposed nonconvex PBCD algorithm extends to handling problems with multiple variables, as supported by theoretical analysis. Experimental evaluations, spanning various image low-level and high-level vision tasks such as inpainting, classification, and clustering, validate the effectiveness and efficiency of our framework across diverse databases. The source code is available at https://github.com/ZhangHengMin/FNPBCD_LR.In a nutshell, our framework provides a unified solution to tackle both low-level and high-level vision tasks in images. By combining fast nonconvex low-rank matrix learning with adaptive parameter updates, we achieve efficient computation, yielding high-quality results that demonstrate robustness against various types of noise. The evaluations further endorse the reliability and applicability of our proposed framework.

A warm-start FE-dABCD algorithm for elliptic optimal control problems with constraints on the control and the gradient of the state

In this paper, elliptic control problems with the integral constraint on the gradient of the state and the box constraint on the control are considered. The optimality conditions for the problem are proved. To numerically solve the problem, a finite element duality-based inexact majorized accelerated block coordinate descent (FE-dABCD) algorithm is proposed. Specifically, both the state and the control are discretized by piecewise linear functions. An inexact majorized ABCD algorithm is employed to solve the discretized problem via its dual, which is a multi-block unconstrained convex optimization problem, but the primal variables are also generated in each iteration. Thanks to the inexactness of the FE-dABCD algorithm, the subproblems at each iteration are allowed to be solved inexactly. For the smooth subproblem, we use the preconditioned generalized minimal residual (GMRES) method to solve it. For the two nonsmooth subproblems, one of them has a closed form solution through introducing an appropriate proximal term, and another one is solved by the line search Newton's method. Based on these efficient strategies, we prove that our proposed FE-dABCD algorithm enjoys O(1k2) iteration complexity. Moreover, to make the algorithm more efficient and further reduce its computation cost, based on the mesh-independence of ABCD method, we propose an FE-dABCD algorithm with a warm-start strategy (wFE-dABCD). Some numerical experiments are done and the numerical results show the efficiency of the FE-dABCD algorithm and wFE-dABCD algorithm.

Optimal ensemble construction for multistudy prediction with applications to mortality estimation.

It is increasingly common to encounter prediction tasks in the biomedical sciences for which multiple datasets are available for model training. Common approaches such as pooling datasets before model fitting can produce poor out-of-study prediction performance when datasets are heterogeneous. Theoretical and applied work has shown multistudy ensembling to be a viable alternative that leverages the variability across datasets in a manner that promotes model generalizability. Multistudy ensembling uses a two-stage stacking strategy which fits study-specific models and estimates ensemble weights separately. This approach ignores, however, the ensemble properties at the model-fitting stage, potentially resulting in performance losses. Motivated by challenges in the estimation of COVID-attributable mortality, we propose optimal ensemble construction, an approach to multistudy stacking whereby we jointly estimate ensemble weights and parameters associated with study-specific models. We prove that limiting cases of our approach yield existing methods such as multistudy stacking and pooling datasets before model fitting. We propose an efficient block coordinate descent algorithm to optimize the loss function. We use our method to perform multicountry COVID-19 baseline mortality prediction. We show that when little data is available for a country before the onset of the pandemic, leveraging data from other countries can substantially improve prediction accuracy. We further compare and characterize the method's performance in data-driven simulations and other numerical experiments. Our method remains competitive with or outperforms multistudy stacking and other earlier methods in the COVID-19 data application and in a range of simulation settings.

Joint Beamforming Design in Reconfigurable Intelligent Surface-Assisted Rate Splitting Networks

Reconfigurable Intelligent Surface (RIS) is an emerging technology that can improve the spectrum and energy efficiency of next-generation wireless networks. However, attaining accurate channel state information (CSI) for the cascaded RIS channel is particularly challenging. Imperfect CSI is a major bottleneck to achieving the spectral efficiency benefit of RIS-assisted networks. Rate splitting (RS), a promising multiple access technology, has been shown to be able to achieve an improved spectrum efficiency and be robust to channel uncertainties. This paper investigates the interplay between RIS and RS by considering a RIS-assisted RS beamforming problem. Active beamforming at the base station (BS) and passive beamforming at the RIS are jointly considered to maximize the minimum user rate under both the perfect CSI case and the imperfect CSI case. A block coordinate descent (BCD) algorithm is developed to solve this non-convex problem. Compared with the conventional semi-definite relaxation (SDR) approach, the proposed method does not require that the covariance matrix of the common beamforming vector be rank-one. Moreover, we present theoretical results to help reveal the impact of the system parameters and explain the performance gain resulting from the integration of RIS and RS. Extensive simulation results are also provided to show that RIS-assisted RS can improve the max-min rate performance significantly compared with conventional multiple access technologies, such as non-orthogonal multiple access (NOMA) and space division multiple access (SDMA) with/without RIS, especially in overloaded systems. With the proposed method, RS shows great potential in combating realistic CSI errors in RIS-assisted networks.

Coordinated Parenting of Civic Work and Student Management in Colleges and Universities Based on the Correlation Matrix in the Context of Informationization

Abstract In this paper, an association matrix is constructed based on a global self-representation model, and the problem of constructing an association matrix with sparse self-representation of samples and Laplace regularized least squares classifier are integrated to improve the model performance. Based on the block coordinate descent algorithm, iterative solving for each variable was performed to optimize the model, and then the decision-making model was constructed using the multi-objective decision-making algorithm in order to provide managers with appropriate educational and management program services. Finally, the influence of ideology and political education on students’ quality as well as college management is analyzed, and the way of correlation evolution between ideology and politics and student management is explored. The results show that ideology and politics have a positive influence on student quality, and the degree of influence on personal concepts as well as on the pursuit of knowledge and the establishment of goals is 0.75 and 0.8, respectively. The probability that a highly correlated and coordinated college or university with ideology politics and student management will remain in this rank in the following year is 65%, and the probability of downward or upward development is 20% in both cases.

Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model

With the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM), this paper introduces a variable selection method based on exponential square loss and the adaptive lasso penalty. Due to the non-convex and non-differentiable nature of this proposed method, convex programming is not applicable for its solution. We develop a block coordinate descent algorithm, decompose the exponential square component into the difference of two convex functions, and utilize the CCCP algorithm in combination with parabolic interpolation for optimizing problem-solving. Numerical simulations demonstrate that neglecting the spatial effects of error terms can lead to reduced accuracy in selecting zero coefficients in SEM. The proposed method demonstrates robustness even when noise is present in the observed values and when the spatial weights matrix is inaccurate. Finally, we apply the model to the Boston housing dataset.

An iterative algorithm for low‐rank tensor completion problem with sparse noise and missing values

AbstractRobust low‐rank tensor completion plays an important role in multidimensional data analysis against different degradations, such as sparse noise, and missing entries, and has a variety of applications in image processing and computer vision. In this paper, an optimization model for low‐rank tensor completion problems is proposed and a block coordinate descent algorithm is developed to solve this model. It is shown that for one of the subproblems, the closed‐form solution exists and for the other, a Riemannian conjugate gradient algorithm is used. In particular, when all elements are known, that is, no missing values, the block coordinate descent is simplified in the sense that both subproblems have closed‐form solutions. The convergence analysis is established without requiring the latter subproblem to be solved exactly. Numerical experiments illustrate that the proposed model with the algorithm is feasible and effective.

Variable Selection for Sparse Logistic Regression with Grouped Variables

We present a new penalized method for estimation in sparse logistic regression models with a group structure. Group sparsity implies that we should consider the Group Lasso penalty. In contrast to penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting the group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets.

Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model

Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model

Direction of Arrival Estimation With Gain-Phase Uncertainties in Unknown Nonuniform Noise

This paper considers the problem of direction-of-arrival (DOA) estimation for narrowband source signals under the coexistence of gain-phase uncertainties and nonuniform noise. Firstly, by exploiting the low-rank property of the covariance of signal components, and the diagonal property of noise covariance, an optimization problem with low-rank constraints is formulated to estimate the nonuniform noise covariance matrix, which is then solved efficiently by the alternating direction method of multipliers (ADMM). Secondly, a linear transformation operator is employed to construct a rank reduction (RARE) estimator, and subsequently an initial DOA and gain-phase uncertainties are obtained via one-dimensional (1-D) spectral search. With initial estimates, an augmented DOA estimation is finally achieved by constructing a weighted and structured sparse total least-squares (WSS-TLS) optimization problem, which is solved using the block coordinate descent algorithm. Simulation results show the superior performance of the proposed method, and it achieves better tradeoff between computational complexity and performance, compared to existing methods.

Energy-Efficient Joint Collaborative and Passive Beamforming for Intelligent-Reflecting-Surface-Assisted Wireless Sensor Networks

Intelligent reflecting surface (IRS) provides a promising technology that can improve the energy efficiency of wireless communications, by building the controllable wireless propagation environment with the utilization of massive passive reflecting elements. Motivated by this, we apply the IRS to assist the data collection based on collaborative beamforming in Wireless Sensor Networks (WSNs). With the objective to maximize the network lifetime, we present an energy efficient joint collaborative and passive beamforming design for an IRS-assisted WSN, which jointly optimizes the beamforming vector for all nodes and phase shifts for IRS’s reflecting elements. To efficiently resolve the joint optimization problem, we develop a penalty dual decomposition (PDD) based algorithm combined with augmented Lagrangian method, penalty-based method and block coordinate descent algorithm, which decomposes the joint optimization problem into four simplified subproblems. Especially in solving IRS’s phase shifts optimization subproblem, we formulate this subproblem as a quadratically constrained quadratic programming (QCQP) problem and further propose a low computational complexity approximate iteration algorithm to resolve this QCQP problem, which iteratively linearizes this QCQP problem to a sequence of approximate programming with linear equality constraints, whose closed-form solution is presented. Theoretical analysis indicates the proposed algorithm can converge to a KKT solution. Simulation results indicate that the IRS-assisted design and proposed algorithm improve the energy efficiency and prolong the network lifetime as compared to alternative algorithms.

Joint power and subchannel allocation regarding energy harvesting in MC-NOMA based wireless networks

We propose resource allocation schemes for a multi-carrier non-orthogonal multiple access (MC-NOMA) system with the consideration of energy harvesting. The resource allocation schemes includes an optimization scheme for maximizing the total system capacity, and an optimization scheme for maximizing the fairness among users, such that both schemes guarantee minimum data rate and harvested energy to each user. Because NOMA is one of the key technologies for enhancing system capacity, we apply a NOMA scheme to an Energy Harvesting Wireless Network (EHWN) to increase the capacity whilst at the same time supplying sufficient harvested energy and data rate for each user. The proposed resource allocation schemes are based on a block coordinate descent (BCD) algorithm that can effectively solve problems in which the objective function is not jointly concave. The performance of each proposed scheme is evaluated using simulations, and we show that the capacity maximization and fairness schemes outperform orthogonal multiple access (OMA) schemes in terms of capacity and fairness, respectively.

Exploiting NOMA and RIS in Integrated Sensing and Communication

A novel integrated sensing and communication (ISAC) system is proposed, where a dual-functional base station is utilized to transmit the superimposed non-orthogonal multiple access (NOMA) communication signal for serving communication users and sensing targets simultaneously. Furthermore, a new reconfigurable intelligent surface (RIS)-aided-sensing structure, where a dedicated RIS is deployed to provide virtual line-of-sight (LoS) links for radar targets, is also proposed to address the significant path loss or blockage of LoS links for the sensing task. Based on this setup, the beampattern gain at the RIS for the radar target is derived and adopted as a sensing metric. The objective of this paper is to maximize the minimum beampattern gain by jointly optimizing active beamforming at the base station (BS), power allocation coefficients among NOMA users and passive beamforming at the RIS. To tackle the non-convexity of the formulated optimization problem, the beampattern gain and constraints are first transformed into more tractable forms. Then, an iterative block coordinate descent (IBCD) algorithm is proposed by employing successive convex approximation (SCA), Schur complement, semidefinite relaxation (SDR) and sequential rank-one constraint relaxation (SRCR) methods. To reduce the complexity of the proposed IBCD algorithm, a low-complexity iterative alternating optimization (IAO) algorithm is proposed. Particularly, the active beamforming is optimized by solving a semidefinite programming (SDP) problem and the closed-form solutions of the power allocation coefficients are derived. Numerical results show that: i) the proposed RIS-NOMA-ISAC system always outperforms the RIS-ISAC system without NOMA in beampattern gain and illumination power; ii) the low-complexity IAO algorithm achieves a comparable performance to that achieved by the IBCD algorithm. iii) high beampattern gain can be achieved by the proposed joint optimization algorithms in underloaded and overloaded communication scenarios.

Energy-Efficient Maximization for RIS-Aided MISO Symbiotic Radio Systems

Symbiotic radio (SR) and reconfigurable intelligent surface (RIS) can serve as a complementary technique for each other regarding spectrum efficiency and energy efficiency (EE) improvements. In this paper, we investigate a RIS-aided multiple-input single-output SR system with multiple backscatter devices (BDs). In particular, an EE-based maximization resource allocation problem is formulated by jointly optimizing the passive beamforming vector of the RIS, the active beamforming vector of the primary transmitter (PT), and the reflection coefficient of each BD under multiple constraints, including the minimum rate of each user, the maximum transmit power of the PT, and the minimum harvested energy of each BD. To solve the non-convex problem, a Dinkelbach-based block coordinate descent algorithm is developed to obtain the sub-optimal solution. Numerical results verify that the proposed algorithm achieves two times more than the traditional algorithms in terms of system EE.

Joint Reconstruction and Spectrum Refinement for Photon-Counting-Detector Spectral CT.

Photon-counting detector CT (PCD-CT) is a revolutionary technology in decades in the field of CT. Its potential benefits in lowering noise, dose reduction, and material-specific imaging enable completely new clinical applications. Spectral reconstruction of basis material maps requires knowledge of the x-ray spectrum and the spectral response calibration of the detector. However, spectrum estimation errors caused by inaccurate energy threshold calibration will degrade the accuracy of the reconstructions. Existing spectrum estimation methods are not adequately modeled for bias in energy threshold position. Besides, directly solving a big number of variables of the pixel-wise effective spectra for PCD is an ill-conditioned problem so that stable solution is hardly achievable. In this paper, we assumed the effective spectra variation across the detector mainly comes from the calibration error in the energy threshold positions as well as the intrinsic threshold distribution. We propose a joint reconstruction and spectrum refinement algorithm (JoSR) that introduces an innovative spectrum model based on non-negative matrix factorization (NMF) to significantly reduce the dimension of unknowns so that makes the problem well-conditioned. The polychromatic spectral imaging model and the basis material decomposition method together form an optimization objective. The proximal regularized block coordinate descent algorithm is adopted to deal with the non-convex optimization problem to ensure convergence. Simulation studies and experiments on a laboratory PCD-CT system validated the proposed JoSR method. The results demonstrate its advantages on image quality and quantitative accuracy over other state-of-the-art methods in the field.

Waveform Design and Optimization for Integrated Visible Light Positioning and Communication

In this paper, we investigate an energy efficient waveform design for integrated visible light positioning and communication (VLPC) systems by exploiting the relationship between visible light positioning (VLP) and visible light communication (VLC). We propose that the direct current component and the alternating current component of the VLPC signals are utilized for positioning and communication, respectively. With a single LED-lamp, we propose a received-signal-strength based 3D VLP scheme, and further derive the Cramer-Rao lower bound (CRLB). Then, by exploiting the inherent coupling relationship between VLP and VLC, the positioning results are utilized for channel estimation of VLC, which can significantly reduce the channel estimation pilot overhead. Furthermore, we optimize the waveform design by minimizing the CRLB, while satisfying both the outage probability of communication rate and total transmit power constraints. However, this problem turns to be non-convex and intractable. To address this challenging problem, we utilize the Conditional Value-at-Risk to conservatively transform the outage probability constraint into a deterministic form. By exploiting the block coordinate descent algorithm, the waveform design problem can be efficiently solved by alternately optimizing VLP and VLC convex sub-problems and dual problem. Finally, simulation results verify both the effectiveness and robustness of the proposed waveform design.