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Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis

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arXiv 2024年

作者： He, Zhuohang Ma, Junjie Yuan, Xiaojun The National Key Laboratory of Wireless Communications University of Electronic Science and Technology of China Chengdu611731 China The Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100864 China

Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations. © 2024, CC BY.

关键词： Asymptotic analysis

Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

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arXiv 2023年

作者： Yin, Tao Zhang, Lu Zheng, Weiying Zhu, Xiaopeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type (I + T) = f, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth "slow-rise" windowing function is introduced to truncate the boundary integral equations and a "correction" strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Boundary integral equations

Quantized Constant-Envelope Waveform Design for Massive MIMO DFRC Systems

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arXiv 2024年

作者： Wu, Zheyu Liu, Ya-Feng Chen, Wei-Kun Masouros, Christos The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The Department of Electronic and Electrical Engineering University College London Torrington Place LondonWC1E 7JE United Kingdom

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances. Copyright © 2024, The Authors. All rights reserved.

关键词： Mean square error

PIECEWISE LINEAR VALUE FUNCTION APPROXIMATIONS IN NONLINEAR DYNAMIC SCHEDULING PROBLEMS WITH VTOLS

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arXiv 2023年

作者： Nikitina, Viktoriya Rogovs, Sergejs Gerdts, Matthias Institute of Applied Mathematics and Scientific Computing Department of Aerospace Engineering University of the Bundeswehr Munich Germany

Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and observation missions in a military context. This article presents an efficient numerical framework for dynamic scheduling of multiple VTOLs. It combines a scheduling problem with optimal trajectory planning. The whole setting is formulated as a mixed-integer bilevel optimization problem. At the upper level, VTOLs are scheduled, and their starting times are computed. The solution of the lower level problem involves the computation of a value function and yields optimal trajectories for every aerial vehicle. In order to solve the bilevel problem, it is recast into a single-level one. The resulting mixed-integer nonlinear program (MINLP) is then piecewise linearized and solved numerically by a linear solver based on the Branch-and-Bound algorithm. Numerical results prove the feasibility of the approach proposed in this work. © 2023, CC BY.

关键词： Integer programming

MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS

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Journal of computational mathematics 2021年第3期39卷 453-470页

作者： Xiaodi Zhang Weiying Zheng LSEC NCMISInstitute of Computational Mathermatics and Scientific ComputingAcademy of Mathematics and Systerns ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China

In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic *** propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic *** turns out to be robust for relatively large physical *** extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.

关键词： Monolithic multigrid Magnetohydrodynamic equations Diagonal Braess-Sarazin smoother Finite element method

FINITE ELEMENT ERROR ESTIMATES FOR THE NONLINEAR SCHRÖDINGER-POISSON MODEL

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arXiv 2023年

作者： Cui, Tao Lu, Wenhao Pan, Naiyan Zheng, Weiying LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Science University of Chinese Academy of Sciences Beijing100190 China

In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schrödinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To establish the error estimate, we present a unified theory of error estimates for a class of nonlinear problems. The theory is based on three conditions: 1) the original problem has a solution u which is the fixed point of a compact operator A, 2) A is Fréchet-differentiable at u and I − A′[u] has a bounded inverse in a neighborhood of u, and 3) there exists an operator Ah which converges to A in the neighborhood of u. The theory states that Ah has a fixed point uh which solves the approximate problem. It also gives the error estimate between u and uh, without assumptions on the well-posedness of the approximate problem. We apply the unified theory to the finite element approximation of the Schrödinger-Poisson model and obtain optimal error estimate between the numerical solution and the exact solution. Numerical experiments are presented to verify the convergence rates of numerical *** Codes 65M60, 65L15, 37L65 Copyright © 2023, The Authors. All rights reserved.

关键词： Approximation theory

Statistical Multiplexing Gain Analysis of Centralized Open Radio Access Networks with Limited Cells and Heterogeneous Traffics

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IEEE Transactions on Vehicular Technology 2025年

作者： Wang, Lu Zhou, Yiqing Liu, Ya-Feng Liu, Ling Shi, Ningzhe Tian, Lin Shi, Jinglin National Key Laboratory of Transient Impact Beijing102202 China 208 Research Institute of China Ordnance Industries Beijing102202 China Chinese Academy of Sciences State Key Lab of Processors Institute of Computing Technology Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Beijing Key Laboratory of Mobile Computing and Pervasive Device Beijing100190 China Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Chinese Academy of Sciences Institute of Computing Technology Beijing100190 China Nanjing Institute of InforSuperBahn Nanjing211100 China

Centralized open radio access networks (O-RANs) aggregate computing resources of multiple cells to improve resource utilization and achieve statistical multiplexing gain (SMG), i.e., the ratio of the number of deployed resources (DepR) for distributed radio access network (D-RAN) to that for O-RAN. SMG of O-RAN has been investigated with infinite number of cells with homogeneous bursty-temporal traffic features. However, in practice, the number of cells is limited, and in the era of Internet of Things (IoT), cells with heterogeneous bursty-temporal traffics (het-traffics), should be considered. This paper analyzes the SMG of O-RAN with limited het-traffic cells. First of all, given traffic models of het-traffic cells following different bursty lognormal distribution and periodic time-varying features, required resources (ReqR) for D-RAN can be derived. Then, to obtain the distribution of ReqR for O-RAN with limited het-traffic cells, a Gaussian mixture model (GMM) based resource distribution approximation (GMM-RDA) is proposed. Thus SMG can be obtained for any given service rate. In simulations, the effectiveness of GMM-RDA is verified by Kolmogorov-Smirnov (K-S) test, and the accuracy of achieved SMG can be up to 99.7%, which is about 33% higher than that obtained by the law of large numbers (LLN) for infinite cells. Moreover, het-traffic cells resulting from service diversification can enhance SMG in O-RAN by 34.7%. © 1967-2012 IEEE.

关键词： Radio access networks

Subspace method based on neural networks for eigenvalue problems

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arXiv 2024年

作者： Dai, Xiaoying Fan, Yunying Sheng, Zhiqiang LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China

With the rapid development of machine learning, numerical discretization methods based on deep neural networks have been widely used in many fields, especially in solving high-dimensional problems where traditional methods face bottlenecks. However, for low-dimensional problems, existing machine learning methods are not as accurate and efficient as traditional methods. In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. Our basic idea is to use neural network based basis functions to span a subspace, then calculate the parameters of the neural network based basis functions through appropriate training, and finally calculate the Galerkin projection of the eigenvalue problem onto the subspace and obtain an approximate solution. In addition, we reduce the dimension of the subspace by applying some dimensionality reduction technique, which can improve the accuracy of the approximate solution in further. Numerical experiments show that we can obtain approximate eigenvalues with accuracy of 10−11 but with less then 400 epochs, which is significantly superior to other existing neural network based *** Codes 65N25, 65L15, 68T07 Copyright © 2024, The Authors. All rights reserved.

关键词：

An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

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arXiv 2023年

作者： Chen, Wei-Kun Wu, Zheyu Zhang, Rui-Jin Liu, Ya-Feng Dai, Yu-Hong Luo, Zhi-Quan The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined;and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality. Copyright © 2023, The Authors. All rights reserved.

关键词： Resource allocation