凸优化在信号处理与通信中的应用Convex Optimization in Signal Processing and Communications
凸优化理论在信号处理以及通信系统中的应用 比较经典的通信系统凸优化入门教程ContentsList of contributorspage IxPrefaceAutomatic code generation for real- time convex optimizationJacob Mattingley and stephen Boyd1.1 Introduction1.2 Solvers and specification languages61. 3 Examples121. 4 Algorithm considerations1.5 Code generation261.6 CVXMOD: a preliminary implementation281.7 Numerical examples291. 8 Summary, conclusions, and implicationsAcknowledgments35ReferencesGradient-based algorithms with applications to signal-recoveryproblemsAmir beck and marc teboulle2.1 Introduction422.2 The general optimization model432.3 Building gradient-based schemes462. 4 Convergence results for the proximal-gradient method2.5 A fast proximal-gradient method2.6 Algorithms for l1-based regularization problems672.7 TV-based restoration problems2. 8 The source-localization problem772.9 Bibliographic notes83References85ContentsGraphical models of autoregressive processes89Jitkomut Songsiri, Joachim Dahl, and Lieven Vandenberghe3.1 Introduction893.2 Autoregressive processes923.3 Autoregressive graphical models983. 4 Numerical examples1043.5 Conclusion113Acknowledgments114References114SDP relaxation of homogeneous quadratic optimization: approximationbounds and applicationsZhi-Quan Luo and Tsung-Hui Chang4.1 Introduction1174.2 Nonconvex QCQPs and sDP relaxation1184.3 SDP relaxation for separable homogeneous QCQPs1234.4 SDP relaxation for maximization homogeneous QCQPs1374.5 SDP relaxation for fractional QCQPs1434.6 More applications of SDP relaxation1564.7 Summary and discussion161Acknowledgments162References162Probabilistic analysis of semidefinite relaxation detectors for multiple-input,multiple-output systems166Anthony Man-Cho So and Yinyu Ye5.1 Introduction1665.2 Problem formulation1695.3 Analysis of the SDr detector for the MPsK constellations1725.4 Extension to the Qam constellations1795.5 Concluding remarks182Acknowledgments182References189Semidefinite programming matrix decomposition, and radar code design192Yongwei Huang, Antonio De Maio, and Shuzhong Zhang6.1 Introduction and notation1926.2 Matrix rank-1 decomposition1946.3 Semidefinite programming2006.4 Quadratically constrained quadratic programming andts sdp relaxation201Contents6.5 Polynomially solvable QCQP problems2036.6 The radar code-design problem2086.7 Performance measures for code design2116.8 Optimal code design2146.9 Performance analysis2186.10 Conclusions223References226Convex analysis for non-negative blind source separation withapplication in imaging22Wing-Kin Ma, Tsung-Han Chan, Chong-Yung Chi, and Yue Wang7.1 Introduction2297.2 Problem statement2317.3 Review of some concepts in convex analysis2367.4 Non-negative, blind source-Separation criterion via CAMNS2387.5 Systematic linear-programming method for CAMNS2457.6 Alternating volume-maximization heuristics for CAMNS2487.7 Numerical results2527.8 Summary and discussion257Acknowledgments263References263Optimization techniques in modern sampling theory266Tomer Michaeli and yonina c. eldar8.1 Introduction2668.2 Notation and mathematical preliminaries2688.3 Sampling and reconstruction setup2708.4 Optimization methods2788.5 Subspace priors2808.6 Smoothness priors2908.7 Comparison of the various scenarios3008.8 Sampling with noise3028. 9 Conclusions310Acknowledgments311References311Robust broadband adaptive beamforming using convex optimizationMichael Rubsamen, Amr El-Keyi, Alex B Gershman, and Thia Kirubarajan9.1 Introduction3159.2 Background3179.3 Robust broadband beamformers3219.4 Simulations330Contents9.5 Conclusions337Acknowledgments337References337Cooperative distributed multi-agent optimization340Angelia Nedic and asuman ozdaglar10.1 Introduction and motivation34010.2 Distributed-optimization methods using dual decomposition34310.3 Distributed-optimization methods using consensus algorithms35810.4 Extensions37210.5 Future work37810.6 Conclusions38010.7 Problems381References384Competitive optimization of cognitive radio MIMO systems via game theory387Gesualso Scutari, Daniel P Palomar, and Sergio Barbarossa11.1 Introduction and motivation38711.2 Strategic non-cooperative games: basic solution concepts and algorithms 39311.3 Opportunistic communications over unlicensed bands411.4 Opportunistic communications under individual-interferenceconstraints4151.5 Opportunistic communications under global-interference constraints43111.6 Conclusions438Ackgment439References43912Nash equilibria: the variational approach443Francisco Facchinei and Jong-Shi Pang12.1 Introduction44312.2 The Nash-equilibrium problem4412. 3 EXI45512.4 Uniqueness theory46612.5 Sensitivity analysis47212.6 Iterative algorithms47812.7 A communication game483Acknowledgments490References491Afterword494Index49ContributorsSergio BarbarossaYonina c, eldarUniversity of rome-La SapienzaTechnion-Israel Institute of TechnologyHaifaIsraelAmir beckTechnion-Israel instituteAmr El-Keyiof TechnologyAlexandra universityHaifEgyptIsraelFrancisco facchiniStephen boydUniversity of rome La sapienzaStanford UniversityRomeCaliforniaItalyUSAAlex b, gershmanTsung-Han ChanDarmstadt University of TechnologyNational Tsing Hua UniversityDarmstadtHsinchuGermanyTaiwanYongwei HuangTsung-Hui ChangHong Kong university of scienceNational Tsing Hua Universityand TechnologyHsinchuHong KongTaiwanThia KirubarajanChong-Yung chiMcMaster UniversityNational Tsing Hua UniversityHamilton ontarioHsinchuCanadaTaiwanZhi-Quan LuoJoachim dahlUniversity of minnesotaanybody Technology A/sMinneapolisDenmarkUSAList of contributorsWing-Kin MaMichael rebsamenChinese University of Hong KongDarmstadt UniversityHong KonTechnologyDarmstadtAntonio de maioGermanyUniversita degli studi di napoliFederico iiGesualdo scutariNaplesHong Kong University of Sciencealyand TechnologyHong KongJacob MattingleyAnthony Man-Cho SoStanford UniversityChinese University of Hong KongCaliforniaHong KongUSAJitkomut songsinTomer michaeliUniversity of californiaTechnion-Israel instituteLoS Angeles. CaliforniaogyUSAHaifaMarc teboulleTel-Aviv UniversityAngelia NedicTel-AvUniversity of Illinois atIsraelUrbana-ChampaignInoSLieven VandenbergheUSAUniversity of CaliforniaLos Angeles, CaliforniaUSAAsuman OzdaglarMassachusetts Institute of TechnologyYue WangBoston massachusettsVirginia Polytechnic InstituteUSAand State UniversityArlingtonDaniel p palomarUSAHong Kong University ofScience and TechnologyYinyu YeHong KongStanford UniversityCaliforniaong-Shi PangUSAUniversity of illinoisat Urbana-ChampaignShuzhong zhangIllinoisChinese university of Hong KongUSAHong KongPrefaceThe past two decades have witnessed the onset of a surge of research in optimization.This includes theoretical aspects, as well as algorithmic developments such as generalizations of interior-point methods to a rich class of convex-optimization problemsThe development of general-purpose software tools together with insight generated bythe underlying theory have substantially enlarged the set of engineering-design problemsthat can be reliably solved in an efficient manner. The engineering community has greatlybenefited from these recent advances to the point where convex optimization has nowemerged as a major signal-processing technique on the other hand, innovative applica-tions of convex optimization in signal processing combined with the need for robust andefficient methods that can operate in real time have motivated the optimization commu-nity to develop additional needed results and methods. The combined efforts in both theoptimization and signal-processing communities have led to technical breakthroughs ina wide variety of topics due to the use of convex optimization This includes solutions tonumerous problems previously considered intractable; recognizing and solving convex-optimization problems that arise in applications of interest; utilizing the theory of convexoptimization to characterize and gain insight into the optimal-solution structure and toderive performance bounds; formulating convex relaxations of difficult problems; anddeveloping general purpose or application-driven specific algorithms, including thosethat enable large-scale optimization by exploiting the problem structureThis book aims at providing the reader with a series of tutorials on a wide varietyof convex-optimization applications in signal processing and communications, writtenby worldwide leading experts, and contributing to the diffusion of these new developments within the signal-processing community. The goal is to introduce convexoptimization to a broad signal-processing community, provide insights into how convexoptimization can be used in a variety of different contexts, and showcase some notablesuccesses. The topics included are automatic code generation for real-time solvers, graphical models for autoregressive processes, gradient-based algorithms for signal-recoveryapplications, semidefinite programming(SDP)relaxation with worst-case approximationperformance, radar waveform design via SDP, blind non-negative source separation forimage processing, modern sampling theory, robust broadband beamforming techniquesdistributed multiagent optimization for networked systems, cognitive radio systems viagame theory, and the variational-inequality approach for Nash-equilibrium solutionsPrefaceThere are excellent textbooks that introduce nonlinear and convex optimization, providing the reader with all the basics on convex analysis, reformulation of optimizationproblems, algorithms, and a number of insightful engineering applications. This book istargeted at advanced graduate students, or advanced researchers that are already familiarwith the basics of convex optimization. It can be used as a textbook for an advanced graduate course emphasizing applications, or as a complement to an introductory textbookthat provides up-to-date applications in engineering. It can also be used for self-study tobecome acquainted with the state of-the-art in a wide variety of engineering topicsThis book contains 12 diverse chapters written by recognized leading experts worldwide, covering a large variety of topics. Due to the diverse nature of the book chaptersit is not possible to organize the book into thematic areas and each chapter should betreated independently of the others. a brief account of each chapter is given nextIn Chapter 1, Mattingley and Boyd elaborate on the concept of convex optimizationin real-time embedded systems and automatic code generation. As opposed to genericsolvers that work for general classes of problems, in real-time embedded optimization thesame optimization problem is solved many times, with different data, often with a hardreal-time deadline. Within this setup the authors propose an automatic code-generationsystem that can then be compiled to yield an extremely efficient custom solver for theproblem familyIn Chapter 2, Beck and Teboulle provide a unified view of gradient-based algorithmsfor possibly nonconvex and non-differentiable problems, with applications to signalrecovery. They start by rederiving the gradient method from several different perspectives and suggest a modification that overcomes the slow convergence of the algorithmThey then apply the developed framework to different image-processing problems suchas e1-based regularization, TV-based denoising, and Tv-based deblurring, as well ascommunication applications like source localizationIn Chapter 3, Songsiri, Dahl, and Vandenberghe consider graphical models for autore-gressive processes. They take a parametric approach for maximum-likelihood andmaximum-entropy estimation of autoregressive models with conditional independenceconstraints, which translates into a sparsity pattern on the inverse of the spectral-densitymatrix. These constraints turn out to be nonconvex. To treat them the authors proposea relaxation which in some cases is an exact reformulation of the original problem. Theproposed methodology allows the selection of graphical models by fitting autoregressiveprocesses to different topologies and is illustrated in different applicationsThe following three chapters deal with optimization problems closely related to SDPand relaxation techniquesIn Chapter 4, Luo and Chang consider the SDP relaxation for several classes ofquadratic-optimization problems such as separable quadratically constrained quadraticprograms(QCQPs)and fractional QCQPs, with applications in communications and signal processing. They identify cases for which the relaxation is tight as well as classes ofquadratic-optimization problems whose relaxation provides a guaranteed, finite worstcase approximation performance. Numerical simulations are carried out to assess theefficacy of the SDP-relaxation approach
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企业级大数据知识图谱产品的构建及应用
企业级大数据知识图谱产品的构建及应用 明略鹚据MININGLAMP企业级大数据做啥?Big data is like teenage sexEveryone talks about it, nobody really knows how to do itEveryone thinks everyone else is doing it,so everyone claims they are doing it tooSimon matthews卖平台?卖数据?卖服务?做咨询????Arch Summit全球架构师峰会Powered by InfoQ明略据· MININGLAMP从业务的角度看公安公安搜索团伙挖掘重大事件预金融报表计算用户画像实时交易反欺诈历史数据精准营销设备故障造业查询预测电商税务数据整合数据治理推荐系统税务反欺诈社交,O20大数据商业智能数据驱动的平台(BI资源变现普通需求中高级需求高级且痛点需求普通需求很通用,基本无行业属性,但业务附加值低越高级的需求,行业属性越明显,越难落地或做岀好效果,但业务附加值高能解决高级需求的产品或方案,往往也能解决普通、中级高级需求,但反之未必Arch Summit全球架构师峰会Powered by InfoQ明略据· MININGLAMP明略之道多种多样的需求公安金融制造业需求需求需求升级思考降维打击交互式服务批量式可视化业机务公安金融构建数据之间的关联知学数据数据简洁统一的数据模型只习降维打击最关键的两点:数据治理/整合和关联计算业务知识和机器学习(数据挖掘)会贯穿整个流程普适的方案,目标是解决各行业最难的业务需求Arch Summit全球架构师峰会Powered by InfoQ明略鹚据· MININGLAMP构建大数据知识图谱产品企业级大数据简析构建大数据知识图谱产品应用浅谈Arch Summit全球架构师峰会Powered by InfoQ明略据· MININGLAMP知识图谱是什么?o 8以图为载体点代表“实体”边代表“关系●●a88●结合特定行业数据和领域知识,得到的则是领域內知识图谱比如,银行+交易数据+人员信息=>以人为核心(交易为关系)的知识图谱Arch Summit全球架构师峰会Powered by InfoQ明略鹚据·· MININGLAMF个简单的工商企业的知识图谱轮胎生产总经理公司A人属于法人公司关联万物互联子公司制造业产品属于法人公司==B行业手套图上每个点皆为“实体”,边为“关系”(具有不同的类别)实体和关系可以有多个属性(如人年龄,性别,关系类别/开始时间万物互联”,数据种类越多,数据量越大,越能还原真实世界的面貌Arch Summit全球架构师峰会Powered by InfoQ明略据· MININGLAMP如何落地知识图谱产品?交互式服务|批量式服务|可视化服务提供各类服务接口,支撑业务场景数据挖掘与机器学习业务模型,自然语言处理,全量数据机器学习图数据库知识图谱的物理载体,提供各类图相关服务关联计算基于规则的关联计算,建立实体之间的关系数据治理与整合结构化与非结构化数据智能治理与整合他统一数据视图建立行业特定的知识图谱所需的数据模型Arch Summit全球架构师峰会Powered by InfoQ明略据· MININGLAMP多规融合数据模型姓张三人车张二实体手机公司产品特别的,对于实体,需要融合实体各方面的信息D110105**实大交易流水人员地址XX市XX街道酒店入住事件火车出行手机159*为**为民航出行139**大直系关系关系人户关系信XXX人案关系Arch Summit全球架构师峰会Powered by InfoQ
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