Efficient multiuser detector based on box-constrained dichotomous coordinate descent and regularization

The presented iterative multiuser detection technique was based on joint deregularized and box-constrained solution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated algorithm.The deregularization maximized the energy of the solution,which was opposite to the Tikhonov regularization where the energy was minimized.However,combined with box-constraints,the deregularization forced the solution to be close to the binary set.It further exploited the box-constrained dichotomous coordinate descent algorithm and adapted it to the nonstationary iterative Tikhonov regularization to present an efficient detector.As a result,the worst-case and average complexity are reduced down as K2.8 and K2.5 floating point operation per second,respectively.The development improves the "efficient frontier" in multiuser detection,which is illustrated by simulation results.In addition,most operations in the detector are additions and bit-shifts.This makes the proposed technique attractive for fixed-point hardware implementation.

Temperature Prediction Model Identification Using Cyclic Coordinate Descent Based Linear Support Vector Regression

Temperature prediction plays an important role in ring die granulator control,which can influence the quantity and quality of production. Temperature prediction modeling is a complicated problem with its MIMO, nonlinear, and large time-delay characteristics. Support vector machine( SVM) has been successfully based on small data. But its accuracy is not high,in contrast,if the number of data and dimension of feature increase,the training time of model will increase dramatically. In this paper,a linear SVM was applied combing with cyclic coordinate descent( CCD) to solving big data regression. It was mathematically strictly proved and validated by simulation. Meanwhile,real data were conducted to prove the linear SVM model's effect. Compared with other methods for big data in simulation, this algorithm has apparent advantage not only in fast modeling but also in high fitness.

A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.

A BLOCK-COORDINATE DESCENT METHOD FOR LINEARLY CONSTRAINED MINIMIZATION PROBLEM

In this paper, a block coordinate descent method is developed to solve a linearly constrained separable convex optimization problem. The proposed method divides the decision variable into a few blocks based on certain rules. Then the candidate solution is iteratively obtained by updating one block at each iteration. The problem, whether or not there are overlapping regions between two immediately adjacent blocks, is investigated. The global convergence of the proposed method is established under some suitable assumptions. Numerical results show that the proposed method is effective compared with some ＂full-type＂ methods.

Synchronous Parallel Block Coordinate Descent Method for Nonsmooth Convex Function Minimization

This paper proposes a synchronous parallel block coordinate descent algorithm for minimizing a composite function,which consists of a smooth convex function plus a non-smooth but separable convex function.Due to the generalization of the proposed method,some existing synchronous parallel algorithms can be considered as special cases.To tackle high dimensional problems,the authors further develop a randomized variant,which randomly update some blocks of coordinates at each round of computation.Both proposed parallel algorithms are proven to have sub-linear convergence rate under rather mild assumptions.The numerical experiments on solving the large scale regularized logistic regression with 1 norm penalty show that the implementation is quite efficient.The authors conclude with explanation on the observed experimental results and discussion on the potential improvements.

Improved Variable Forgetting Factor Proportionate RLS Algorithm with Sparse Penalty and Fast Implementation Using DCD Iterations

The proportionate recursive least squares(PRLS)algorithm has shown faster convergence and better performance than both proportionate updating(PU)mechanism based least mean squares(LMS)algorithms and RLS algorithms with a sparse regularization term.In this paper,we propose a variable forgetting factor(VFF)PRLS algorithm with a sparse penalty,e.g.,l_(1)-norm,for sparse identification.To reduce the computation complexity of the proposed algorithm,a fast implementation method based on dichotomous coordinate descent(DCD)algorithm is also derived.Simulation results indicate superior performance of the proposed algorithm.

Joint Optimization for on-Demand Deployment of UAVs and Spectrum Allocation in UAVs-Assisted Communication

To improve the efficiency and fairness of the spectrum allocation for ground communication assisted by unmanned aerial vehicles(UAVs),a joint optimization method for on-demand deployment and spectrum allocation of UAVs is proposed,which is modeled as a mixed-integer non-convex optimization problem(MINCOP).An algorithm to estimate the minimum number of required UAVs is firstly proposed based on the pre-estimation and simulated annealing.The MINCOP is then decomposed into three sub-problems based on the block coordinate descent method,including the spectrum allocation of UAVs,the association between UAVs and ground users,and the deployment of UAVs.Specifically,the optimal spectrum allocation is derived based on the interference mitigation and channel reuse.The association between UAVs and ground users is optimized based on local iterated optimization.A particle-based optimization algorithm is proposed to resolve the subproblem of the UAVs deployment.Simulation results show that the proposed method could effectively improve the minimum transmission rate of UAVs as well as user fairness of spectrum allocation.

UAV-assisted cooperative offloading energy efficiency system for mobile edge computing

Reliable communication and intensive computing power cannot be provided effectively by temporary hot spots in disaster areas and complex terrain ground infrastructure.Mitigating this has greatly developed the application and integration of UAV and Mobile Edge Computing(MEC)to the Internet of Things(loT).However,problems such as multi-user and huge data flow in large areas,which contradict the reality that a single UAV is constrained by limited computing power,still exist.Due to allowing UAV collaboration to accomplish complex tasks,cooperative task offloading between multiple UAVs must meet the interdependence of tasks and realize parallel processing,which reduces the computing power consumption and endurance pressure of terminals.Considering the computing requirements of the user terminal,delay constraint of a computing task,energy constraint,and safe distance of UAV,we constructed a UAV-Assisted cooperative offloading energy efficiency system for mobile edge computing to minimize user terminal energy consumption.However,the resulting optimization problem is originally nonconvex and thus,difficult to solve optimally.To tackle this problem,we developed an energy efficiency optimization algorithm using Block Coordinate Descent(BCD)that decomposes the problem into three convex subproblems.Furthermore,we jointly optimized the number of local computing tasks,number of computing offloaded tasks,trajectories of UAV,and offloading matching relationship between multi-UAVs and multiuser terminals.Simulation results show that the proposed approach is suitable for different channel conditions and significantly saves the user terminal energy consumption compared with other benchmark schemes.

An Efficient Federated Learning Framework Deployed in Resource-Constrained IoV:User Selection and Learning Time Optimization Schemes

In this article,an efficient federated learning(FL)Framework in the Internet of Vehicles(IoV)is studied.In the considered model,vehicle users implement an FL algorithm by training their local FL models and sending their models to a base station(BS)that generates a global FL model through the model aggregation.Since each user owns data samples with diverse sizes and different quality,it is necessary for the BS to select the proper participating users to acquire a better global model.Meanwhile,considering the high computational overhead of existing selection methods based on the gradient,the lightweight user selection scheme based on the loss decay is proposed.Due to the limited wireless bandwidth,the BS needs to select an suitable subset of users to implement the FL algorithm.Moreover,the vehicle users’computing resource that can be used for FL training is usually limited in the IoV when other multiple tasks are required to be executed.The local model training and model parameter transmission of FL will have significant effects on the latency of FL.To address this issue,the joint communication and computing optimization problem is formulated whose objective is to minimize the FL delay in the resource-constrained system.To solve the complex nonconvex problem,an algorithm based on the concave-convex procedure(CCCP)is proposed,which can achieve superior performance in the small-scale and delay-insensitive FL system.Due to the fact that the convergence rate of CCCP method is too slow in a large-scale FL system,this method is not suitable for delay-sensitive applications.To solve this issue,a block coordinate descent algorithm based on the one-step projected gradient method is proposed to decrease the complexity of the solution at the cost of light performance degrading.Simulations are conducted and numerical results show the good performance of the proposed methods.

Variable selection via generalized SELO-penalized linear regression models

The seamless-L0 （SELO） penalty is a smooth function on [0, ∞） that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, we first generalize SELO to a class of penalties retaining good features of SELO, and then propose variable selection and estimation in linear models using the proposed generalized SELO （GSELO） penalized least squares （PLS） approach. We show that the GSELO-PLS procedure possesses the oracle property and consistently selects the true model under some regularity conditions in the presence of a diverging number of variables. The entire path of GSELO-PLS estimates can be efficiently computed through a smoothing quasi-Newton （SQN） method. A modified BIC coupled with a continuation strategy is developed to select the optimal tuning parameter. Simulation studies and analysis of a clinical data are carried out to evaluate the finite sample performance of the proposed method. In addition, numerical experiments involving simulation studies and analysis of a microarray data are also conducted for GSELO-PLS in the high-dimensional settings.

Multiple phase detector of M-ary phase shift keying symbols in code division multiple access systems

A novel iterative technique, the phase descent search detection was proposed. This technique constrained the solution （PDS） algorithm, for M-ary phase shift keying （M-PSK） symbols to have a unit magnitude and it was based on coordinate descent iterations where coordinates were the unknown symbol phases. The PDS algorithm, together with a descent local search （also implemented as a version of the PDS algorithm）, was used multiple times with different initializations in a proposed multiple phase detector; the solution with the minimum cost was then chosen as the final solution. The simulation results show that for highly loaded multiuser scenarios, the proposed technique has a detection performance that is close to the single-user bound. The results also show that the multiple phase detector allows detection in highly overloaded scenarios and it exhibits near-far resistance. In particular, the detector has a performance that is significantly better, and complexity that is significantly lower, than that of the detector based on semi-definite relaxation.

Hooke and Jeeves algorithm for linear support vector machine

Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine （SVM）, at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves algorithm which adds pattern search after every iteration in coordinate descent method was applied to SVM and a global Newton algorithm was used to solve one-variable subproblems. We proved the convergence of the algorithm. Experimental results show Hooke and Jeeves＇ method does accelerate convergence specially for final convergence and achieves higher testing accuracy more quickly in classification.

Efficient multiuser detector based on box-constrained deregularization and its FPGA design

Multiuser detection can be described as a quadratic optimization problem with binary constraint. Many techniques are available to find approximate solution to this problem. These tech- niques can be characterized in terms of complexity and detection performance. The ＂efficient frontier＂ of known techniques include the decision-feedback, branch-and-bound and probabilistic data association detectors. The presented iterative multiuser detection technique is based on joint deregularized and box-constrained so- lution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated algorithm. The deregulari- zation maximizes the energy of the solution, this is opposite to the Tikhonov regularization where the energy is minimized. However, combined with box-constraints, the deregularization forces the solution to be close to the binary set. We further exploit the box- constrained dichotomous coordinate descent （DCD） algorithm and adapt it to the nonstationary iterative Tikhonov regularization to present an efficient detector. As a result, the worst-case and aver- age complexity are reduced down to K28 and K2~ floating point operation per second, respectively. The development improves the ＂efficient frontier＂ in multiuser detection, which is illustrated by simulation results. Finally, a field programmable gate array （FPGA） design of the detector is presented. The detection performance obtained from the fixed-point FPGA implementation shows a good match to the floating-point implementation.

A parallel complex divider architecture based on DCD iterations for computing complex division in MVDR beamformer

This paper presents a hardware architecture using mixed pipeline and parallel processing for complex division based on dichotomous coordinate descent(DCD) iterations. The objective of the proposed work is to achieve low-latency and resource optimized complex divider architecture in adaptive weight computation stage of minimum variance distortionless response(MVDR)algorithm. In this work, computation of complex division is modeled as a 2×2 linear equation solution problem and the DCD algorithm allows linear systems of equations to be solved with high degree of computational efficiency. The operations in the existing DCD algorithm are suitably parallel pipelined and the performance is optimized to 2 clock cycles per iteration. To improve the degree of parallelism, a parallel column vector read architecture is devised.The proposed work is implemented on the field programmable gate array(FPGA) platform and the results are compared with state-of-art literature. It concludes that the proposed architecture is suitable for complex division in adaptive weight computation stage of MVDR beamformer. We demonstrate the performance of the proposed architecture for MVDR beamformer employed in medical ultrasound imaging applications.

基于两部模型的组合惩罚似然估计方法研究及其应用

在统计学中,多借助零膨胀模型研究零膨胀数据潜在的模型结构及变量选择问题。然而,在多数情况下,响应变量的非零部分为定量数据,简单的零膨胀模型无法刻画这类数据的模型结构,对应的参数估计方法也不再适用。鉴于此,学者提出处理零膨胀半连续数据的两部模型。本文将组合惩罚似然估计方法引入两部模型,研究其变量选择问题。提出一种新的处理高维统计分析问题的惩罚似然估计方法:NCPM (New Combined Punishment Method),并将该方法应用于太原市降水量数据,分析其影响因素。模拟及实例分析结果均表明本文的方法行之有效,较传统的惩罚似然估计方法具有更高的预测精度。

Energy Efficiency Maximization for Cooperative NOMA with Hardware Impairments

The massive connectivity and limited energy pose significant challenges to deploy the enormous devices in energy-efficient and environmentally friendly in the Internet of Things(IoT).Motivated by these challenges,this paper investigates the energy efficiency(EE)maximization problem for downlink cooperative non-orthogonal multiple access(C-NOMA)systems with hardware impairments(HIs).The base station(BS)communicates with several users via a half-duplex(HD)amplified-and-forward(AF)relay.First,we formulate the EE maximization problem of the system under HIs by jointly optimizing transmit power and power allocated coefficient(PAC)at BS,and transmit power at the relay.The original EE maximization problem is a non-convex problem,which is challenging to give the optimal solution directly.First,we use fractional programming to convert the EE maximization problem as a series of subtraction form subproblems.Then,variable substitution and block coordinate descent(BCD)method are used to handle the sub-problems.Next,a resource allocation algorithm is proposed to maximize the EE of the systems.Finally,simulation results show that the proposed algorithm outperforms the downlink cooperative orthogonal multiple access(C-OMA)scheme.

Near-surface velocity inversion from Rayleigh wave dispersion curves based on a differential evolution simulated annealing algorithm

The utilization of urban underground space in a smart city requires an accurate understanding of the underground structure.As an effective technique,Rayleigh wave exploration can accurately obtain information on the subsurface.In particular,Rayleigh wave dispersion curves can be used to determine the near-surface shear-wave velocity structure.This is a typical multiparameter,high-dimensional nonlinear inverse problem because the velocities and thickness of each layer must be inverted simultaneously.Nonlinear methods such as simulated annealing(SA)are commonly used to solve this inverse problem.However,SA controls the iterative process though temperature rather than the error,and the search direction is random;hence,SA always falls into a local optimum when the temperature setting is inaccurate.Specifically,for the inversion of Rayleigh wave dispersion curves,the inversion accuracy will decrease with an increasing number of layers due to the greater number of inversion parameters and large dimension.To solve the above problems,we convert the multiparameter,highdimensional inverse problem into multiple low-dimensional optimizations to improve the algorithm accuracy by incorporating the principle of block coordinate descent(BCD)into SA.Then,we convert the temperature control conditions in the original SA method into error control conditions.At the same time,we introduce the differential evolution(DE)method to ensure that the iterative error steadily decreases by correcting the iterative error direction in each iteration.Finally,the inversion stability is improved,and the proposed inversion method,the block coordinate descent differential evolution simulated annealing(BCDESA)algorithm,is implemented.The performance of BCDESA is validated by using both synthetic data and field data from western China.The results show that the BCDESA algorithm has stronger global optimization capabilities than SA,and the inversion results have higher stability and accuracy.In addition,synthetic data analysis also shows that BCDESA can avoid the problems of the conventional SA method,which assumes the S-wave velocity structure in advance.The robustness and adaptability of the algorithm are improved,and more accurate shear-wave velocity and thickness information can be extracted from Rayleigh wave dispersion curves.

An Improved Robust Sparse Convex Clustering

Convex clustering,turning clustering into a convex optimization problem,has drawn wide attention.It overcomes the shortcomings of traditional clustering methods such as K-means,Density-Based Spatial Clustring of Applications with Noise(DBSCAN)and hierarchical clustering that can easily fall into the local optimal solution.However,convex clustering is vulnerable to the occurrence of outlier features,as it uses the Frobenius norm to measure the distance between data points and their corresponding cluster centers and evaluate clusters.To accurately identify outlier features,this paper decomposes data into a clustering structure component and a normalized component that captures outlier features.Different from existing convex clustering evaluating features with the exact measurement,the proposed model can overcome the vast difference in the magnitude of different features and the outlier features can be efficiently identified and removed.To solve the proposed model,we design an efficient algorithm and prove the global convergence of the algorithm.Experiments on both synthetic datasets and UCI datasets demonstrate that the proposed method outperforms the compared approaches in convex clustering.

An Alternating Direction Method of Multipliers for MCP-penalized Regression with High-dimensional Data

The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.

Energy-efficient data collection for UAV-assisted IoT: Joint trajectory and resource optimization

Internet of Things(IoT) can be conveniently deployed while empowering various applications, where the IoT nodes can form clusters to finish certain missions collectively. As energyefficient operations are critical to prolong the lifetime of the energy-constrained IoT devices, the Unmanned Aerial Vehicle(UAV) can be dispatched to geographically approach the IoT clusters towards energy-efficient IoT transmissions. This paper intends to maximize the system energy efficiency by considering both the IoT transmission energy and UAV propulsion energy, where the UAV trajectory and IoT communication resources are jointly optimized. By applying largesystem analysis and Dinkelbach method, the original fractional optimization is approximated and reformulated in the form of subtraction, and further a block coordinate descent framework is employed to update the UAV trajectory and IoT communication resources iteratively. Extensive simulation results are provided to corroborate the effectiveness of the proposed method.