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Max-Min Fairness in IRS-Aided Multi-Cell MISO Systems with Joint Transmit and Reflective Beamforming

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arXiv 2020年

作者： Xie, Hailiang Xu, Jie Liu, Ya-Feng School of Information Engineering Guangdong University of Technology Guangzhou510006 China Shenzhen518172 China 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

This paper investigates an intelligent reflecting surface (IRS)-aided multi-cell multiple-input single-output (MISO) system with a set of multi-antenna base stations (BSs) each communicating with a single-antenna user, in which an IRS is dedicatedly deployed for assisting the wireless transmission and suppressing the inter-cell interference. Under this setup, we jointly optimize the coordinated transmit beamforming vectors at the BSs and the reflective beamforming vector at the IRS, for the purpose of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) at the users, subject to the individual maximum transmit power constraints at the BSs and the reflection constraints at the IRS. To solve the non-convex min-weighted-SINR maximization problem, we first present an exact-alternating-optimization approach to optimize the transmit and reflective beamforming vectors in an alternating manner, in which the transmit and reflective beamforming optimization subproblems are solved exactly in each iteration by using the techniques of second-order-cone program (SOCP) and semi-definite relaxation (SDR), respectively. However, the exact-alternating-optimization approach has high computational complexity, and may lead to compromised performance due to the uncertainty of randomization in SDR. To avoid these drawbacks, we further propose an inexact-alternating-optimization approach, in which the transmit and reflective beamforming optimization subproblems are solved inexactly in each iteration based on the principle of successive convex approximation (SCA). In addition, to further reduce the computational complexity, we propose a low-complexity inexact-alternating-optimization design, in which the reflective beamforming optimization subproblem is solved more inexactly. Via numerical results, it is shown that the proposed three designs achieve significantly increased min-weighted-SINR values, as compared with benchmark schemes without the IRS or with random re

关键词： Beamforming

An efficient quadratic programming relaxation based algorithm for large-scale MIMO detection

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arXiv 2020年

作者： Zhao, Ping-Fan Li, Qing-Na Chen, Wei-Kun Liu, Ya-Feng School of Mathematics and Statistics Beijing Institute of Technology Beijing China School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing China 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 Beijing China

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve small-scale problems, the proposed algorithm is demonstrated to be competitive with the state-of-the-art approaches in terms of detection accuracy and solution efficiency;when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power *** Codes 90C2

关键词： Quadratic programming

Convergence rate of inertial forward-backward splitting algorithms based on the local error bound condition

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arXiv 2020年

作者： Liu, Hongwei Wang, Ting Liu, Zexian School Of Mathematics And Statistics Xidian University Xi'An710126 China State Key Laboratory Of Scientific And Engineering Computing Institute Of Computational Mathematics And Scientific/Engineering Computing AMSS Chinese Academy Of Sciences Beijing100190 China School Of Mathematics And Statistics Guizhou University Guiyang550025 China

The " Inertial Forward-Backward algorithm " (IFB) is a powerful tool for convex nonsmooth minimization problems, and under the local error bound condition, the R-linear convergence rates for the sequences of objective values and iterates have been proved if the inertial parameter γksatisfies supkγkkγk= 1 is not know. In this paper, based on the local error bound condition, we exploit a new assumption condition for the important parameter tkin IFB, which implies that limk→∞γk= 1, and establish the convergence rate of function values and strong convergence of the iterates generated by the IFB algorithms with six tksatisfying the above assumption condition in Hilbert space. It is remarkable that, under the local error bound condition, we show that the IFB algorithms with some tkcan achieve sublinear convergence rate of o(1/kp) for any positive integer p > 1. In addition, we propose a class of Inertial Forward-Backward algorithm with adaptive modification and show it has same convergence results as IFB under the error bound condition. Some numerical experiments are conducted to illustrate our results. Copyright © 2020, The Authors. All rights reserved.

关键词： Parameter estimation

A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

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arXiv 2021年

作者： Xi, Yingxia Ji, Xia Zhang, Shuo School of Science Nanjing University of Science and Technology Nanjing210094 China School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to *** Codes 31A30, 65N30, 47B07 Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

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arXiv 2021年

作者： Dai, Xiaoying Pan, Yan Yang, Bin Zhou, Aihui 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 NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity. Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

HETEROGENEOUS MULTISCALE METHODS FOR FOURTH-ORDER SINGULAR PERTURBATIONS

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arXiv 2025年

作者： Liao, Yulei Ming, Pingbing Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore119076 Singapore LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models for architectured materials. We establish an error estimate for the homogenized solution applicable to general media and derive an explicit convergence for the locally periodic media with the fine-scale Ε. For cell problems of size δ = NΕ, the classical resonance error O(Ε/δ) can be eliminated due to the dominance of the higher-order operator. Despite the occurrence of boundary layer effects, discretization errors do not necessarily deteriorate for general boundary conditions. Numerical simulations corroborate these theoretical findings. Copyright © 2025, The Authors. All rights reserved.

关键词： Convergence of numerical methods

Complexity Analysis and Algorithm Design of Pooling Problem

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Journal of the Operations Research Society of China 2018年第2期6卷 249-266页

作者： Yu-Hong Dai Rui Diao Kai Fu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The pooling problem,also called the blending problem,is fundamental in production planning of *** can be formulated as an optimization problem similar with the minimum-cost flow ***,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general *** also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of *** this paper,we prove that the pooling problem is still strongly NP-hard even with only one *** means the quality is an essential difference between minimum-cost flow problem and the pooling *** solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming *** convergence of the algorithm is *** numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local *** results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

关键词： Pooling problem Complexity analysis Successive linear programming Non-monotone

A New Global Divergence Free and Pressure-Robust HDG Method for Tangential Boundary Control of Stokes Equations

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arXiv 2022年

作者： Chen, Gang Gong, Wei Mateos, Mariano Singler, John R. Zhang, Yangwen School of Mathematics Sichuan University Chengdu China NCMIS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Dpto. de Matemáticas Universidad de Oviedo Campus de Gijón Spain Department of Mathematics and Statistics Missouri University of Science and Technology RollaMO United States Department of Mathematical Science Carnegie Mellon University PittsburghPA United States

In [ESAIM: M2AN, 54(2020), 2229-2264], we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control that reflects its global regularity. However, the error estimates depend on the pressure, and the velocity is not divergence free. The importance of pressure-robust numerical methods for fluids was addressed by John et al. [SIAM Review, 59(2017), 492-544]. In this work, we devise a new HDG method to approximate the solution of the Stokes tangential boundary control problem;the HDG method is also of independent interest for solving the Stokes equations. This scheme yields a H(div) conforming, globally divergence free, and pressure-robust solution. To the best of our knowledge, this is the first time such a numerical scheme has been obtained for an optimal boundary control problem for the Stokes equations. We also provide numerical experiments to show the performance of the new HDG method and the advantage over the non pressure-robust *** Codes 35Q35, 49M25, 65N30 Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

Layer-splitting methods for time-dependent Schrödinger equations of incommensurate systems

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arXiv 2021年

作者： Wang, Ting Chen, Huajie Zhou, Aihui Zhou, Yuzhi School of Mathematical Sciences Beijing Normal University Beijing100875 China 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 CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

This work considers numerical methods for the time-dependent Schrödinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that results in semidiscrete differential equations with extremely demanding computational cost. We propose several fully discrete time stepping schemes based on the idea of "layer-splitting", which decompose the semidiscrete problem into sub-problems that each corresponds to one of the periodic layers. Then these schemes handle only some periodic systems in the original lower dimension at each time step, which reduces the computational cost significantly and is natural to involve stochastic methods and parallel computing. Both theoretical analysis and numerical experiments are provided to support the reliability and efficiency of the algorithms. Copyright © 2021, The Authors. All rights reserved.

关键词： Numerical methods