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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模糊理论和神经网络的基础与应用.pdf
模糊理论和神经网络的基础资料，相关知识说得较明白易懂。模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)中国计算机学会学术著作丛书模糊理论和神经网络的基础与应用Introduction to Fuzzy Theory andNeural Networks and Their Application赵振宇徐用恐著清华大学出版社广西科学技术出版社模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)(京)新登字158号(桂)新登字06号内容简介模糊理论和神经网弊是近年来得到迅速发展的嘶兴学料,它们的应用和影响己经遍及人工智能算机科学自动控制、专家系统信息科学、 CAD/CAN医疗诊断、经济等部门和领域本书系统驰论述了模糊理论和神经网络的基本理论、方法,从统一的工程角度综合分析了两大学科的最新成果,研究动向以及两者交叉部分中的前沿研究并介绍了高技术的应用实例。全书非14章,分三大都分第一部分为模糊理论的基础、建模方法和实际应用第二部升为神经网将的基本理论罔络学习方法和典型实倒第三部分讨论了模棚系统和神经网络系统的异同、融合和相互转换方法,本书还提供了大暈劑颞,以便读者自己模伤实践加深理解。本书可供白动控制计算机、信号信息处理、电路与系统、系綻工程等专业的高校师生利科技人虽遄用版权所有,醐印必究。本书封面貼有消华大学出版社激光防伪标签,无标签者不得销嘗肉书在版編目(CIP數据模糊理论和神经网络的基础与应用=Ⅰ NTRODUCTION TO FUZZY THEORY ANDNEURAL NETWORKS AND THEIR APPLI CATTON/赵振宇,徐用懋著.一北京:清华大学出版社,1995.19〔中国计算机学会学术者作丛书IsHN7-302-02061-2I.模r.①赵…闪徐…】,①模糊数学-应用-计算机网络②神经网络应川计算机网终Ⅳ.TP393中国版本图书馆CIP数据核字(95)第23616号出版者:清华大学出版社(北京清华大学校内,邮编100084)西科学技术出版社(厂西南宁河堤路14号,邮编530021印刷者:北京市清华园印刷厂发行者:新华书店总店北京科披发行所开本:787×1092116印张;13.75字数:324千字版次:i996年6月第1版199日年6月第1次印刷号:IN7-302-020612/TP·958印数:001-4000定价:16.00元模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)清华大学出版社广西科学抆术出版社计算机学术著作出版基金评审委员会主任委员张效祥副主任委员周远清汪成为委员王鼎兴杨芙清李三立施伯乐徐家福夏培肃董韫美张兴强徐培忠模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)出版说明近午来随岩微电子和计算相技术渗透到各个技术领域,人类正在步入一个技术迅插发展的新时期。这个新时期的主要标志是计算机和信息处理的广泛应用。计算机在改造传统产业实现管理自动化促进新兴产业的发展等方面都起着重要作用,它在现代化建设中的战略地位愈来盒明显。算机科学与其它学科的交叉又产生了许多新学科推功着科学技术向更广阔的领域发展,正在对人类社会产生深远的影响科学技术是第一生产力。计算机科学技术是我国高科技领域的一个重要方面。为了推动我国计算机科学及产业的发展,促进学术交流,使科研慮果尽快转化为生产力华大学出版杜与广西科学技术出版社联合设立了“计算机学术著作基金”,旨在支持和员科技人员,提写高水平的学术著作,以反映和推广我国在这一领域的最新成果计算机学术著作出版基金资助出版的著作范国包括:有重要理论价值或重要应用价值的学术专著计算机学科前沿探索的论著推动计算机拔水及产业发的专著;与计算机有关的交叉学科的论蓍有较大应用价值的工具书世界名著的优透翻译作品。凡经作者本人申请,计算机学术著作出版基金评审委员会评牢通过的著作,将由该基金资助出版,出版社将努力徹好出版工作基金还支持两社列选的国家高科技葷点图书和国家教委重獻图书规划中计算机学科领域的学术著作的出版为了做好选题工作出版社特邀请“中国计算机学会”“中国中文信息学会”帮助做好组织有关学术普作丛书的列选工作。热诚希望得到厂大计算机界同仁的支持和帮助清华大学出版社计算机学术著作出版基金办公室西科学技术出版社1992年4月模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)丛书序亩计算机是当代发展最为迅猛的科学技术其应用几乎已深入到人类社会活动和生活的一切领域大大提高了社会生产力引起了经济结构社会结构和生活方式的深刻变化和变革,是最为活跃的生产力之一。计算机本嘉在国际范围内已成为年产值达250亿美元的巨大产业国际争异常剧烈,预计到本世纪末将发展为世界第一大产业。计算帆科技具有极大的综合性质,与众多科学技术相交叉而反过来又渗入更多的科学技术,促进它们的发展。计算机科技内容十分丰富学科分支生长尤为迅速,日新月异,层出不穷。因此在我国计算机科技尚比较落后的情况下加强计算机科技的传播实为当务之急。中国计算机学会一直把出版图书刊物作为学术动的重要内容之一。我国计算机专家学者通过科学实践做出了大量成果积累了丰富经验与学识。他们有撰写著作的大积极性,但相当时期以来计算机学术著作出于印数不多,出版往往退到不少困难,专业性越强有深度的著作出版难度越大最近清华大学出版杜与西科学枝术出版社为促进我国计算机科学技术及产业的发椎动计算机科技著作的出版工作,特设立“计算机学术著作出版基金”,以支持我国计算机科技工作者撰写高水平的学术著作并将资助出版的著作列为中国计算机学会的学术荷作从书我们十分盒视这件事,并三把它列为学会本屈理事会的工作要点之一。我们希望这一系划丛书能对传播学术成果,交流学术愿想促进科转化为生产力起到良好作月能对我国计算积科技发展具有有益的导向意义,也希望我国广大学会会员和计算机和技工作者括海外工作和学习的神州学人们能积极投稿,出好这一系列丛书。中国计算机学会1992年4月20日模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)Introduction to Fuzzy Theory, Neural Networks sand Their Applicationsby Zhen-Yu Zhao and Yong-Mao XuThe fields of fuzzy sets and neural networks have made rapid progress in recentyears, This book gives a comprehensive presentation on recent developments in boththeory and applications, Special emphasis is placed on basic concepts, system designnalysis and development methods of fuzzy systems and neural network systemsThis hook consists of three majar parts. The first two parts present the fundamen-tals and real world applications of fuzzy sets theory and ueural nel works, respectivelyThe last part addresses various state-of-the-art techniques o combine fuzzy logic withneural networks eliminating the disadvantages of each of these technologies while effec-tively combining their advantageshis book can be used as the text for an advanced course on fuzzy theory and neuraletworks. It is also a valuable reference to all researchers and engi eers interested inthese subjects模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)序非高兴得知赵振宇博士和除月懋教投巴完成他们的合著《棋糊理论利神兰网络的基础与应用》近年来模糊理论和神经网络提供了行之有效的方法来解决在特定环境以及采用定性描述方式的多冒的设计中的各种间题这本节从模糊埋论利神网络的基出发,综合分析和归纳了两领域的研究成果,并附有大量的应用实例赵博士和徐教授对棋糊系统和神经网络研究较深,这次他们对此专题的合著正合时宜。此外,赵博土还利用他精通语和英讦的特长,充分收纳了这两大领域的最新发展和动向。二十余年前,L, A. Zadeh教提出的模棚集合哩论已在工程的众多领域中得到广泛深入的研究。对于实际操作人员,即没有精确的数据和过程模型他也能操作和控制复杂的过程。而模糊理论正是将掘作人员的操作经骏鞍换成可以在计算机上运行的掉制算法以便实现模糊控制樸糊控制已泛应用于水质控制她铁操作汽车减震和牵引以及摄泉机聚焦等系统中。人工神经网络是由大量并行分布、有机相联的神经元构成的计算机构,对这种计算机构的研究受启于生物神纸系统的学习能力和并行机制。近年米,对神经网络方面的研究受到愈来愈密切的关注,特别在人工智能、心理学、工程学和物理学等学科中显得空前的活跃。另外,应用神经网络技术的商业产品亦愈来愈多,典型的例子如:语言识别系统爆炸检测器和飞机座位订票系统等绒合模糊理论、神经网络以及其它智能算法(如人上邀传斧法)的研究和应用将有卡常广阔的前景。一个明显的例子就是结合神网络的学习能力来训练基于模糊规则的系统。此书在这方面已有深刻的反映。作者正从统一的角度综合闯述了惯糊理论和抻经网络的重大课题和应用。我相信,此书对行志于模糊理论和神纸网络研究的读者是有裨益Masayos hi tomizuka美圈加州怕党莱大学机械系教授模糊理论和神经网络的基础与应用(仅供交流学习使用,请勿用于商业交易,否则后果自负)FOREWORDI am very pleased that Dr. Zhen-Yu Zhao and Professor Yong-Mao Xu have completed theit book," Introduction to Fuzy Theory, Neural Networks, and Their Appli-cations. In recent years, the fuzzy theory and neural networks have demonstrated theiryaludc for providing solutiont ta problems in unccrtain and imprecise environments a3well as to those with multi-design objectives, which may be stated in a qualitative man-ner. This book starts with Fundamentals of fuzzy theory and neural networks, developsthe ideas for comprehensive coverage of the two sub jects and presents their applications. Having rich rcscarch experienec in fuzzy systcms and neural nerworks, Dr. Zharand Professor Xu make an ideal team to write a book on these subjects. D. Zhao hastaken an advantage of his mastery of two ianguages, Japanese and English. Many recentimporcant developmerts in fuzzy thcory and neural networks havc bcen rcportcd in thesctwo languagesThe theory of fuzzy set&, established by Professor L, A. Zadeh about 20 years agohas been extensively studied in varicus fields of engineering. It is well known that hu-man beings have an ability to operate and control complicated processes without havingprecise data and plant models, Fuzzy theary has been shown to translate such knowldge of human beings into computer implementable control algorithms which are ronmonly called"fuzzy control. "Fuzzy control has been used in many practical applicalionssuch as water quality control, subway operation systems, automotive suspension andraction control and camcorder fotusing and stabilizationArtificial neural networks are computing architectures that consist of massiveparallel interconnections of simple neural proCessors. The study of such architectureshas becn inspired by thc learning abilities and parallelism of biological nervous syatemsIn recent years, neura! networks have received considerable Attention and are now beingactively explored in the fields of artificial intelligence psychology engineering andphysics. Neural networks have been applied to many conmercial products such asspeech recognition systems, explosive detectors and airline seat allocation systerms.Ambitned use af fuzzy theory neural networks, as well as other computational in-telligence algorithms such as genetic algotithms, has heen recognized as being promising, An obvious example is the training of fuzzy rule-based systems ly using the learm
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