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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

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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

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FINITE ELEMENT ERROR ESTIMATES FOR THE NONLINEAR SCHRÖDINGER-POISSON MODEL

arXiv

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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

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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

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Subspace method based on neural networks for eigenvalue problems

arXiv

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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：

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

arXiv

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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

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Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations

引用

Science China mathematics 2020年第1期63卷 39-60页

作者： Mohammed Harunor Rashid Ya-xiang Yuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Faculty of ScienceUniversity of Rajshahi 6205Bangladesh

Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:U→Y is a nonsmooth function and F:X■Y is a set-valued mapping with closed *** introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this ***,under the point-based approximation of f on U and metrically regular property of f+F,we present quadratic rate of convergence of this ***,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+F is metrically *** example of nonsmooth functions that have p-point-based approximation is ***,a numerical experiment is given which illustrates the theoretical result.

关键词： set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation

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NEW C0 INTERIOR PENALTY METHOD FOR MONGE-AMPÈRE EQUATIONS

arXiv

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arXiv 2024年

作者： Chu, Tianyang Guo, Hailong Zhang, Zhimin LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematics and Statistics The University of Melbourne ParkvilleVIC3010 Australia Department of Mathematics Wayne State University DetroitMI48202 United States

Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the C0 interior penalty method to approximation the viscosity solution of the Monge-Ampère equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates. © 2024, CC BY.

关键词： Partial differential equations

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Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model

arXiv

引用

arXiv 2023年

作者： Xie, Peng-Cheng Yuan, Ya-Xiang State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China University of Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China

Derivative-free optimization (DFO) problems are optimization problems where the derivative information is unavailable. The least Frobenius norm updating quadratic interpolation model function is one of the essential under-determined model functions for model-based derivative-free trust-region methods. This article proposes derivative-free optimization with transformed objective functions (DFOTO) and gives a model-based trust-region method with the least Frobenius norm model. The model updating formula is based on Powell’s formula and can be easily implemented. The method shares the same framework with those for problems without transformations, and its query scheme is given. We propose the definitions related to optimality-preserving transformations to understand the interpolation model in our method when minimizing transformed objective functions. We prove the existence of model optimality-preserving transformations beyond translation transformations. The necessary and sufficient condition for such transformations is given. An interesting discovery is that, as a fundamental transformation, the affine transformation with a (non-trivial) positive multiplication coefficient is not model optimality-preserving. We also analyze the corresponding least Frobenius norm updating model and its interpolation error when the objective function is affinely transformed. The convergence property of a provable algorithmic framework containing the least Frobenius norm updating quadratic model for minimizing transformed objective functions is given. Numerical results show that our method can successfully solve most test problems with objective optimality-preserving transformations, even though some of such transformations will change the optimality of the model function. To our best knowledge, this is the first work providing the model-based derivative-free algorithm and analysis for transformed problems with the function evaluation oracle. This article also proposes the "moving-targe

关键词： Interpolation

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A New Two-dimensional Model-based Subspace Method for Large-scale Unconstrained Derivative-free Optimization: 2D-MoSub

arXiv

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arXiv 2023年

作者： Xie, Pengcheng Yuan, Ya-Xiang State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu No.55 Beijing China University of Chinese Academy of Sciences Zhong Guan Cun Donglu No.55 Beijing China

This paper proposes the method 2D-MoSub (2-dimensional model-based subspace method), which is a novel derivative-free optimization (DFO) method based on the subspace method for general unconstrained optimization and especially aims to solve large-scale DFO problems. Our method combines 2-dimensional quadratic interpolation models and trust-region techniques to iteratively update the points and explore the 2-dimensional subspace. Its framework includes initialization, constructing the interpolation set, building the quadratic interpolation model, performing trust-region trial steps, and updating the trust-region radius and subspace. We introduce the framework and computational details of 2D-MoSub, and discuss the poisedness and quality of the interpolation set in the corresponding 2-dimensional subspace. We also analyze some properties of our method, including the model’s approximation error with projection property and the algorithm’s convergence. Numerical results demonstrate the effectiveness and efficiency of 2D-MoSub for solving a variety of unconstrained optimization *** Codes 90C56, 90C30, 65K05, 90C90 Copyright © 2023, The Authors. All rights reserved.

关键词： Interpolation

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