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Sample Approximation-Based Deflation Approaches for Chance SINR-Constrained Joint Power and Admission Control

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Sample Approximation-Based Deflation Approaches for Chance S...

作者： Liu, Ya-Feng Hong, Mingyi Song, Enbin State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing100190 China Iowa State University AmesIA50011 United States Department of Mathematics Sichuan University Chengdu610064 China

Consider the joint power and admission control (JPAC) problem for a multiuser single-input single-output (SISO) interference channel. Most existing works on JPAC assume the perfect instantaneous channel state information (CSI). In this paper, we consider the JPAC problem with the imperfect CSI, i.e., we assume that only the channel distribution information (CDI) is available. We formulate the JPAC problem into a chance (probabilistic)-constrained program, where each link's SINR outage probability is enforced to be less than or equal to a specified tolerance. To circumvent the computational difficulty of the chance SINR constraints, we propose to use the sample (scenario) approximation scheme to convert them into finitely many simple linear constraints. Furthermore, we reformulate the sample approximation of the chance SINR-constrained JPAC problem as a composite group sparse minimization problem and then approximate it by a second-order cone program (SOCP). The solution of the SOCP approximation can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure (the deflation approach). We exploit the special structure of the SOCP approximation and custom-design an efficient algorithm for solving it. Finally, we illustrate the effectiveness and efficiency of the proposed sample approximation-based deflation approaches by simulations. © 2016 IEEE.

关键词： Channel state information

TIGHTNESS OF A NEW AND ENHANCED SEMIDEFINITE RELAXATION FOR MIMO DETECTION

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arXiv 2017年

作者： LU, CHENG LIU, YA-FENG ZHANG, WEI-QIANG ZHANG, SHUZHONG School of Economics and Management North China Electric Power University 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 Beijing100190 China Department of Electronic Engineering Tsinghua University Beijing100084 China Department of Industrial and Systems Engineering University of Minnesota MinneapolisMN55455 United States

In this paper, we consider a fundamental problem in modern digital communications known as multiple-input multiple-output (MIMO) detection, which can be formulated as a complex quadratic programming problem subject to unit-modulus and discrete argument constraints. Various semidefinite relaxation (SDR) based algorithms have been proposed to solve the problem in the literature. In this paper, we first show that the conventional SDR is generally not tight for the problem. Then, we propose a new and enhanced SDR and show its tightness under an easily checkable condition, which essentially requires the level of the noise to be below a certain threshold. The above results have answered an open question posed by So in [35]. Numerical simulation results show that our proposed SDR significantly outperforms the conventional SDR in terms of the relaxation gap. Copyright © 2017, The Authors. All rights reserved.

关键词： Quadratic programming

Optimal Estimation of Sensor Biases for Asynchronous Multi-Sensor Data Fusion

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arXiv 2017年

作者： Pu, Wenqiang Liu, Ya-Feng Yan, Junkun Liu, Hongwei Luo, Zhi-Quan National Laboratory of Radar Signal Processing Collaborative Innovation Center of Information Sensing and Understanding Xidian University Xi'an710071 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 Shenzhen Research Institute of Big Data Chinese University of Hong Kong Shenzhen518100 China

An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the global and local coordinate systems as well as the measurement asynchrony from different sensors. In this paper, we propose a novel nonlinear least squares (LS) formulation for the problem by assuming the existence of a reference target moving with an (unknown) constant velocity. We also propose an efficient block coordinate decent (BCD) optimization algorithm, with a judicious initialization, to solve the problem. The proposed BCD algorithm alternately updates the range and azimuth bias estimates by solving linear least squares problems and semidefinite programs (SDPs). In the absence of measurement noise, the proposed algorithm is guaranteed to find the global solution of the problem and the true biases. Simulation results show that the proposed algorithm significantly outperforms the existing approaches in terms of the root mean square error (RMSE). Copyright © 2017, The Authors. All rights reserved.

关键词： Mean square error

A semi-smooth newton method for solving semidefinite programs in electronic structure calculations

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arXiv 2017年

作者： Li, Yongfeng Wen, Zaiwen Yang, Chao Yuan, Yaxiang Beijing International Center for Mathematical Research Peking University China Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States State Key Laboratory of Scientific and Engineering Computing Academy OfMathematics and Systems Science Chinese Academy of Sciences China

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron wavefunctions. This problem can be formulated as a semidefinite programming problem. Due the large size of the problem, the well-known interior point method can only be used to tackle problems with a few atoms. First-order methods such as the the alternating direction method ofmultipliers (ADMM) have much lower computational cost per iteration. However, their convergence can be slow, especially for obtaining highly accurate approximations. In this paper, we present a practical and efficient second-order semi-smooth Newton type method for solving the SDP formulation of the energy minimization problem. We discuss a number of techniques that can be used to improve the computational efficiency of the method and achieve global convergence. Extensive numerical experiments show that our approach is competitive to the state-of-the-art methods in terms of both accuracy and speed. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational efficiency

Network slicing for service-oriented networks under resource constraints

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arXiv 2017年

作者： Zhang, Nan Liu, Ya-Feng Farmanbar, Hamid Chang, Tsung-Hui Hong, Mingyi Luo, Zhi-Quan School of Mathematical Sciences Peking University 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 Huawei Canada Research Center Ottawa Canada Department of Electrical and Computer Engineering University of Minnesota United States Shenzhen Research Institute of Big Data Chinese University of Hong Kong Shenzhen China

To support multiple on-demand services over fixed communication networks, network operators must allow flexible customization and fast provision of their network resources. One effective approach to this end is network virtualization, whereby each service is mapped to a virtual subnetwork providing dedicated on-demand support to network users. In practice, each service consists of a prespecified sequence of functions, called a service function chain (SFC), while each service function in a SFC can only be provided by some given network nodes. Thus, to support a given service, we must select network function nodes according to the SFC and determine the routing strategy through the function nodes in a specified order. A crucial network slicing problem that needs to be addressed is how to optimally localize the service functions in a physical network as specified by the SFCs, subject to link and node capacity constraints. In this paper, we formulate the network slicing problem as a mixed binary linear program and establish its strong NP-hardness. Furthermore, we propose efficient penalty successive upper bound minimization (PSUM) and PSUM-R(ounding) algorithms, and two heuristic algorithms to solve the problem. Simulation results are shown to demonstrate the effectiveness of the proposed algorithms. Copyright © 2017, The Authors. All rights reserved.

关键词： Network function virtualization

On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization

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On the worst-case complexity of nonlinear stepsize control a...

作者： Grapiglia, G.N. Yuan, J. Yuan, Y. Department of Mathematics Federal University of Paraná Curitiba Brazil State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

A Nonlinear Stepsize Control (NSC) framework has been proposed by Toint [Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization, *** Softw. 28 (2013), pp. 82-95] for unconstrained optimization, generalizing many trust-region and regularization algorithms. More recently, worst-case complexity bounds for the generic NSC framework were proved by Grapiglia et al. [On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization, Math. Program. 152 (2015), pp. 491-520] in the context of non-convex problems. In this paper, improved complexity bounds are obtained for convex and strongly convex objectives. © 2015 Taylor & Francis.

关键词： Optimization

A third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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arXiv 2017年

作者： Wu, Chen Shu, Chang Shi, Baochang Chen, Zhen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore119260 Singapore School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third-order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation LBE based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second-order (or lower-order) of accuracy in time splitting scheme as in the conventional high-order Runge-Kutta (RK) based kinetic methods, the present method solves the original BE, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows. Copyright © 2017, The Authors. All rights reserved.

关键词： Boltzmann equation

A parallel thermal reservoir simulator on distributed-memory supercomputers

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A parallel thermal reservoir simulator on distributed-memory...

SPE Asia Pacific Oil and Gas Conference and Exhibition 2016

作者： Zhong, He Liu, Hui Cui, Tao Wang, Kun Yang, Bo Yang, Min Chen, Zhangxin Dept. of Chemical and Petroleum Engineering University of Calgary 2500 University Drive NW CalgaryAB Canada State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

ISBN: (纸本)9781510835849

This paper describes the algorithms and implementation of a parallel thermal reservoir simulator designed for heavy oil simulation using distributed-memory supercomputers that can solve prohibitive problems efficiently. The thermal simulator inherits the features of a sequential thermal simulator. The performance of supercomputers is proportional to the number of CPUs. As a result, thermal problems can be solved thousands of times faster using supercomputers. This parallel simulator is based on our in-house platform, which provides grid management, data management, linear solvers and a visualization module. The exchange of information between CPUs is achieved by using the message passing interface standard, MPI. Results indicate that this simulator exhibits excellent scalability on the IBM Blue Gene/Q system and is thousands of times faster than serial simulators on a workstation. The simulator is also capable of simulating models with billions of grid blocks and fine resolution results can be obtained. © 2016 Society of Petroleum Engineers. All rights reserved.

关键词： Simulators

Uniqueness and traveling waves in a cell motility model

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arXiv 2017年

作者： Mizuhara, Matthew S. Zhang, Peng Department of Mathematics Pennsylvania State University University ParkPA16802 United States Institute of Natural Sciences Department of Mathematics Shanghai Jiao Tong University Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Ministry of Education 800 Dongchuan Road Shanghai200240 China

We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic cells on a substrate. We establish uniqueness of solutions to the sharp interface limit equation in the so-called subcritical parameter regime. The proof relies on a Grönwall estimate for a specially chosen weighted L2 norm. Next, as persistent motion of crawling cells is of central interest to biologists we study the existence of traveling wave solutions. We prove that traveling wave solutions exist in the supercritical parameter regime provided the non-linear term of the sharp interface limit equation possesses certain asymmetry (related, e.g., to myosin contractility). Finally, we numerically investigate traveling wave solutions and simulate their dynamics. Due to non-uniqueness of solutions of the sharp interface limit equation we simulate a related, singularly perturbed PDE system which is uniquely solvable. Our simulations predict instability of traveling wave solutions and capture both bipedal wandering cell motion as well as rotating cell motion;these behaviors qualitatively agree with recent experimental and theoretical *** Codes 35Q92, 35K55, 65-04 Copyright © 2017, The Authors. All rights reserved.

关键词： Cytology