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Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

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arXiv 2020年

作者： Ma, Ganggang Xu, Jie Liu, Ya-Feng Vedady Moghadam, Mohammad R. Shenzhen China Shenzhen 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 TransferFi Pte Ltd Singapore

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the nonlinear radio frequency (RF) to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the "convex-concave" shape of the RF-DC power relation at ERs. By considering a particular time duration for WPT, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation. In order to solve the non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy harvesting

A brief introduction to manifold optimization

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arXiv 2019年

作者： Hu, Jiang Liu, Xin Wen, Zaiwen Yuan, Yaxiang Beijing International Center for Mathematical Research Peking University China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By utilizing the geometry of manifold, a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold. From this perspective, intrinsic structures, optimality conditions and numerical algorithms for manifold optimization are investigated. Some recent progress on the theoretical results of manifold optimization are also presented. Copyright © 2019, The Authors. All rights reserved.

关键词： Constrained optimization

Asymptotic SEP Analysis and Optimization of Linear-Quantized Precoding in Massive MIMO Systems

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arXiv 2023年

作者： Wu, Zheyu Ma, Junjie Liu, Ya-Feng Swindlehurst, A. Lee 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 Center for Pervasive Communications and Computing University of California IrvineCA92697 United States

A promising approach to deal with the high hardware cost and energy consumption of massive MIMO transmitters is to use low-resolution digital-to-analog converters (DACs) at each antenna element. This leads to a transmission scheme where the transmitted signals are restricted to a finite set of voltage levels. This paper is concerned with the analysis and optimization of a low-cost quantized precoding strategy, referred to as linear-quantized precoding, for a downlink massive MIMO system under Rayleigh fading. In linear-quantized precoding, the signals are first processed by a linear precoding matrix and subsequently quantized component-wise by the DAC. In this paper, we analyze both the signal-to-interference-plus-noise ratio (SINR) and the symbol error probability (SEP) performances of such linear-quantized precoding schemes in an asymptotic framework where the number of transmit antennas and the number of users grow large with a fixed ratio. Our results provide a rigorous justification for the heuristic arguments based on the Bussgang decomposition that are commonly used in prior works. Based on the asymptotic analysis, we further derive the optimal precoder within a class of linear-quantized precoders that includes several popular precoders as special cases. Our numerical results demonstrate the excellent accuracy of the asymptotic analysis for finite systems and the optimality of the derived precoder. Copyright © 2023, The Authors. All rights reserved.

关键词： MIMO systems

Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function

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arXiv 2021年

作者： Wang, Lei Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

In this paper, we focus on the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of d agents. The objective is an average of d local functions, and each function is privately held by an agent and encodes its data. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence, giving rise to high communication costs. In contrast, this paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration. DESTINY combines gradient tracking techniques with a novel approximate augmented Lagrangian function. The global convergence to stationary points is rigorously established. Comprehensive numerical experiments demonstrate that DESTINY has a strong potential to deliver a cutting-edge performance in solving a variety of testing problems. Copyright © 2021, The Authors. All rights reserved.

关键词： Iterative methods

Efficient Parallel Adaptive Computation of 3D Time-Harmonic Maxwell's Equations Using the Toolbox PHG

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Efficient Parallel Adaptive Computation of 3D Time-Harmonic ...

IEEE International Conference on High Performance computing and Communications (HPCC)

作者： Tao Cui State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy and Sciences Beijing China

PHG (parallel hierarchical grid) is a scalable parallel adaptive finite element toolbox under active developmentat the state key laboratory of scientific and engineering computing, Chinese Academy of Sciences. This paper demonstrates its application to adaptive finite element computations of electromagnetic problems. Two examples on solving the time harmonic Maxwell's equations are shown. Results of some large scale adaptive finite element simulations with up to 1 billion degrees of freedom and using up to 2048 CPUs are presented.

关键词： Finite element methods Equations Mathematical model Linear systems Harmonic analysis Algorithm design and analysis Laboratories

The Convergence Properties of Infeasible Inexact Proximal Alternating Linearized Minimization

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arXiv 2022年

作者： Hu, Yukuan Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

The proximal alternating linearized minimization method (PALM) suits well for solving blockstructured optimization problems, which are ubiquitous in real applications. In the cases where subproblems do not have closed-form solutions, e.g., due to complex constraints, infeasible subsolvers are indispensable, giving rise to an infeasible inexact PALM (PALM-I). Numerous efforts have been devoted to analyzing feasible PALM, while little attention has been paid to PALM-I. The usage of PALM-I thus lacks theoretical guarantee. The essential difficulty of analyses consists in the objective value nonmonotonicity induced by the infeasibility. We study in the present work the convergence properties of PALM-I. In particular, we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion. Based upon these, we manage to establish the stationarity of any accumulation point and, moreover, show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property. The prominent advantages of PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3D anisotropic frictional *** Codes 49M27, 65K05, 90C26, 90C30 © 2022, CC BY.

关键词： Linearization

A Variance-Reduced Stochastic Gradient Tracking Algorithm for Decentralized Optimization with Orthogonality Constraints

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arXiv 2022年

Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing approaches leverage the geometric tools from Riemannian optimization to solve this problem at the cost of high sample and communication complexities. To relieve this difficulty, based on two novel techniques that can waive the orthogonality constraints, we propose a variance-reduced stochastic gradient tracking (VRSGT) algorithm with the convergence rate of O(1/k) to a stationary point. To the best of our knowledge, VRSGT is the first algorithm for decentralized optimization with orthogonality constraints that reduces both sampling and communication complexities simultaneously. In the numerical experiments, VRSGT has a promising performance in a real-world autonomous driving application. Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

Error bounded regular algebraic spline curves 99

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Error bounded regular algebraic spline curves

Proceedings of the fifteenth annual symposium on Computational geometry

作者： Chandrajit L. Bajaj Guoliang Xu Department of Computer Science University of Texas Austin TX State Key Laboratory of Scientific and Engineering Computing ICMSEC Chinese Academy of Sciences Beijing

Parallelizable algorithms for optimization problems with orthogonality constraints

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arXiv 2018年

作者： Gao, Bin Liu, Xin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is particularly huge in some application areas such as materials computation. In this paper, we propose a proximal linearized augmented Lagrangian algorithm (PLAM) for solving optimization problems with orthogonality constraints. Unlike the classical augmented Lagrangian methods, in our algorithm, the prime variables are updated by minimizing a proximal linearized approximation of the augmented Lagrangian function, meanwhile the dual variables are updated by a closed-form expression which holds at any first-order stationary point. The orthonormalization procedure is only invoked once at the last step of the above mentioned algorithm if high-precision feasibility is needed. Consequently, the main parts of the proposed algorithm can be parallelized naturally. We establish global subsequence convergence, worst-case complexity and local convergence rate for PLAM under some mild assumptions. To reduce the sensitivity of the penalty parameter, we put forward a modification of PLAM, which is called parallelizable column-wise block minimization of PLAM (PCAL). Numerical experiments in serial illustrate that the novel updating rule for the Lagrangian multipliers significantly accelerates the convergence of PLAM and makes it comparable with the existent feasible solvers for optimization problems with orthogonality constraints, and the performance of PCAL does not highly rely on the choice of the penalty parameter. Numerical experiments under parallel environment demonstrate that PCAL attains good performance and high scalability in solving discretized Kohn-Sham total energy minimization *** Codes 15A18, 65F15, 65K05, 90C06 Copyright © 2018, The Authors. All rights reserved.

关键词： Linearization