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.

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.

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.

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.

A Parallel Line Search Subspace Correction Method for Composite Convex Optimization

In this paper,we investigate a parallel subspace correction framework for composite convex optimization.The variables are first divided into a few blocks based on certain rules.At each iteration,the algorithms solve a suitable subproblem on each block simultaneously,construct a search direction by combining their solutions on all blocks,then identify a new point along this direction using a step size satisfying the Armijo line search condition.They are called PSCLN and PSCLO,respectively,depending on whether there are overlapping regions between two imme-diately adjacent blocks of variables.Their convergence is established under mild assumptions.We compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilai-Borwein step size and the greedy coordinate block descent method for solving the l1-regularized minimization problems.Our numerical results showthatPSCLN andPSCLOcan run fast and return solutions notworse than those from the state-of-theart algorithms on most test problems.It is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures.

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.

An inexact alternating proximal gradient algorithm for nonnegative CP tensor decomposition

Nonnegative tensor decomposition has become increasingly important for multiway data analysis in recent years. The alternating proximal gradient(APG) is a popular optimization method for nonnegative tensor decomposition in the block coordinate descent framework. In this study, we propose an inexact version of the APG algorithm for nonnegative CANDECOMP/PARAFAC decomposition, wherein each factor matrix is updated by only finite inner iterations. We also propose a parameter warm-start method that can avoid the frequent parameter resetting of conventional APG methods and improve convergence performance.By experimental tests, we find that when the number of inner iterations is limited to around 10 to 20, the convergence speed is accelerated significantly without losing its low relative error. We evaluate our method on both synthetic and real-world tensors.The results demonstrate that the proposed inexact APG algorithm exhibits outstanding performance on both convergence speed and computational precision compared with existing popular algorithms.

HAM:a deep collaborative ranking method incorporating textual information

The recommendation task with a textual corpus aims to model customer preferences from both user feedback and item textual descriptions.It is highly desirable to explore a very deep neural network to capture the complicated nonlinear preferences.However,training a deeper recommender is not as effortless as simply adding layers.A deeper recommender suffers from the gradient vanishing/exploding issue and cannot be easily trained by gradient-based methods.Moreover,textual descriptions probably contain noisy word sequences.Directly extracting feature vectors from them can harm the recommender’s performance.To overcome these difficulties,we propose a new recommendation method named the HighwAy reco Mmender(HAM).HAM explores a highway mechanism to make gradient-based training methods stable.A multi-head attention mechanism is devised to automatically denoise textual information.Moreover,a block coordinate descent method is devised to train a deep neural recommender.Empirical studies show that the proposed method outperforms state-of-the-art methods significantly in terms of accuracy.

Reflecting Surface-Aided Device-to-Device Communications System

Intelligent reflecting surface(IRS)is a promising technology for its capability of reflecting the incident signal towards the desired user.IRS can improve the efficiency of wireless communication systems.This paper introduces IRS into a device-to-device(D2D)communications system to improve the throughput of the D2D network.We adopt the block coordinate descent al-gorithm and semidefinite relaxation technique to optimize the beamforming vector,power allocation and phase shift matrix.Simulation results demonstrate that IRS is able to enhance the throughput of the D2D communications system,and the proposed algorithm significantly outper-forms the other benchmark algorithms.

Distributed Intelligent Reflecting Surfaces-Aided Device-to-Device Communications System

Intelligent reflecting surface(IRS)is a revolutionizing and promising technology to improve the high transmission rate of the wireless communication systems.Specifically,an IRS consists of a great amount of low-cost passive reflecting elements,which reflect the incident signals to the desired user by collaboratively using passive beamforming.This paper introduces IRSs into a device-to-device(D2D)underlying cellular system to enhance transmission rate performance of the D2D pairs.We formulate an optimization problem of maximizing the transmission rate of the D2D pairs while satisfying the minimum required rate of the cellular users.We address this problem by jointly optimizing the reuse indicator,received beamforming,power allocation,and phase shift matrices.Block coordinate descent(BCD)algorithm is adopted to decouple the original problem into four subproblems.Closed form solutions are obtained by solving the sub-problems of optimizing the received beamforming and power allocation.Then,Kuhn-Munkres(KM)algorithm and minimization-majorization(MM)algorithm are adopted to solve the sub-problems of optimizing the reuse indicator and phase shift matrices,respectively.Simulation results demonstrate that IRSs can effectively improve the transmission rate of the D2D pairs and our proposed distributed IRSs scheme outperforms the other benchmark schemes.

A Two-stage Adaptive Robust Model for Residential Micro-CHP Expansion Planning

This paper addresses the planning problem of residential micro combined heat and power (micro-CHP) systems (including micro-generation units, auxiliary boilers, and thermal storage tanks) considering the associated technical and economic factors. Since the accurate values of the thermal and electrical loads of this system cannot be exactly predicted for the planning horizon, the thermal and electrical load uncertainties are modeled using a two-stage adaptive robust optimization method based on a polyhedral uncertainty set. A solution method, which is composed of column-and-constraint generation (C&CG) algorithm and block coordinate descent (BCD) method, is proposed to efficiently solve this adaptive robust optimization model. Numerical results from a practical case study show the effective performance of the proposed adaptive robust model for residential micro-CHP planning and its solution method.

On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization

Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.

Aerial intelligent reflecting surface for secure wireless networks:Secrecy capacity and optimal trajectory strategy

This work investigates the potential of the aerial intelligent reflecting surface(AIRS)in secure communication,where an intelligent reflecting surface(IRS)carried by an unmanned aerial vehicle(UAV)is utilized to help the communication between the ground nodes.Specifically,we formulate the joint design of the AIRS’s deployment and the phase shift to maximize the secrecy rate.To solve the non-convex objective,we develop an alternating optimization(AO)approach,where the phase shift optimization is solved by the Riemannian manifold optimization(RMO)method,while the deployment optimization is handled by the successive convex approximation(SCA)technique.Furthermore,to reduce the computational complexity of the RMO method,an element-wise block coordinate descent(EBCD)based method is employed.Simulation results verify the effect of AIRS in improving the communication security,as well as the importance of designing the deployment and phase shift properly.

Coverage Optimization for UAV-Aided Internet of Things with Partial Channel Knowledge

Due to the high maneuverability of unmanned aerial vehicles(UAVs),they have been widely deployed to boost the performance of Internet of Things(IoT).In this paper,to promote the coverage performance of UAV-aided IoT communications,we maximize the minimum average rate of the IoT devices by jointly optimizing the resource allocation strategy and the UAV altitude.Particularly,to depict the practical propagation environment,we take the composite channel model including both the small-scale and the large-scale channel fading into account.Due to the difficulty in acquiring the random small-scale channel fading,we assume that only the large-scale channel sate information is available.On this basis,we formulate an optimization problem,which is not convex and challenging to solve.Then,an efficient iterative algorithm is proposed using block coordinate descent and successive convex optimization tools.Finally,simulation results are presented to demonstrate the significant performance gain of the proposed scheme over existing ones.