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
- 2020-12-10下载
- 积分：1
Java面试笔试题大汇总(最全+详细答案)
搜集的 Java面试笔试题，设置最低积分，备份加供诸位道兄下载，没积分的私我是的内部类,其代码如下所小简单的说,如果整型字面量的值在到之间,那么不会新的对象,而是直接引用常量池中的对象,所以上面的面试题中的结果是而的结果是提醒:越是貌似简单的面试题其中的玄机就越多,需要血试者有相当深厚的功力。和的区别答:运算符有两种用法:按位与;逻辑与ε运算符是短路与运算。逻辑与跟短路与的差别是非常巨人的,虽然二者都要求运算符左右两端的布尔值都是整个表达式的值才是之所以称为短路运算是因为,如果左边的表达式的值是右边的表达式会被直接短路掉,不会进行运算。很多时候我们可能都需要用而不是,例如在验证用户登录时判定用户名不是而且不是空字符串,应当写为:二者的顺序不能交换,更不能用运算符,因为第一个条件如果不成立,根本不能进行字符串的比较,否则会产生异常。注意:逻辑或运算符()和短路或运算符()的差別也是如此。补充:如果你熟悉那你可能更能感受到短路运算的强大,想成为的高手就先从玩转短路运算开始吧3114解释内存中的栈堆和静态区的用法。答:通常我们定义一个基本数据类型的变量,一个对象的引用,还有就是函数调用的现场保存都使用内存中的栈空间;而通过关键字和构造器创建的对象放在堆空间;程序中的字面量()如直接书写的和常量都是放在静杰区中。栈空间操作起来最快但是栈很小,通常大量的对象都是放在堆空间,理论上整个内存没有被其他进程使用的空间甚至硬盘上的虚拟内存都可以被当成堆空间来使用。上面的语句中变量放在栈上,用创建出来的字符串对象放在堆上,而这个字面量放在静态区。补充:较新版本的(从的某个更新开始)中使用了一项叫逃逸分析的技术,可以将一些局部对象放在栈上以提升对象的操作性能等于多少?等于多少?答的返回值是的返回值是。四舍五入的原理是在参数上加然后进行下取整。是否能作用在上,是否能作用在上,是否能作用在上答:在以前,中只能是从开始中引入了枚举类型,也可以是类型,从开始,还可以是字符串(),但是长整型()在目前所有的版本中都是不可以的。、用最有效率的方法计算乘以?答:(左移位相当于乘以的次方,右移位相当于除以的次方)。补充:我们为编写的类重写方法时,可能会看到如下所示的代码,其实我们不太理解为什么要使用这样的乘法运算来产生哈希码(散列码),而且为什么这个数是个素数,为什么通常选择这个数?前两个问题的答案你可以自己百度一下,选择是因为可以用移位和减法运算来代替乘法,从而得到更好的性能。说到这里你可能凵经想到了:等价于左移位相当于乘以的次方再诚去自身就相当于乘以,现在的都能自动完成这个优化4/114、数组有没有方法?有没有方法?答:数组没有方法,有的属性。有方法中,获得字符串的长度是通过属性得到的,这一点容易和混淆。在中,如何跳出当前的多重嵌套循环?答:在最外层循环前加个标记如,然后用可以跳出多重循环。(中支持带标签的和语句,作用有点类似于和中的语句,但是就像要避免使用一样,应该避免使用带标签的和,因为它不会让你的程序变得更优雅,很多时候甚至有相反的作用,所以这种语法其实不知道更好)、构造器()是否可被重写()?答:构造器不能继承,因此不能被重写,但可以被重载。、两个对象值相同但却可有不同的这句话对不对答:不对,如果两个对象和满足,它们的哈希码(相同对于方法和方法是这样规定的:如果两个对象相同(方法返回,那么它们的值一定要相同:如果两个对象的它们并不一定相同。当然,你未必要按照要求去做,但是如果你违背了上述原则就么发在使用容器时,相同的对象可以出现在集合中,同时增加新元素的效率会大大下降(对于使用哈希存储的系统,如果哈希码频繁的冲突将会造成存取性能急剧下降)补充:米于和方法,很多程序都知道,但很多人也就是仅仅知道而己,在的大作《》(很多软件公司,《《编程思想》以及《重构:改善既有代码质量》是程序员必看书籍,如果你还没看过,那就赶紧去亚马逊买一本吧)中是这样介绍方法的:首先方法必须满足自反性(必须返回)、对称性(返回时也必须返回)、传递性(和都返回时,也必须返回)和致性(当和引用的对象信息没有被修改时,多次调用应该得到同样的返回值),而且对于任何非值的引用,必须返回实现高质量的方法的诀窍包括:使用操作符检查参数是否为这个对象的引用;5114使用操作符检查参数是否为正确的类型;对于类中的关键属性,检查参数传入对象的属性是否与之相匹配;编写完方法后,问自己它是否满足对称性、传递性、一致性;重写时总是要重写;不要将方法参数中的对象替换为其他的类型,在重写时不要忘掉注解。、是否可以继承类?答:类是类,不可以被继承。补充:继承本身就是一个错误的行为,对类型最好的重用方式是关联关系)和依赖关系()而不是继承关系()、当一个对象被当作参数传递到一个方法后,此方法可改变这个对象的属性,并可返回变化后的结果,那么这里到底是值传递还是引用传递?答:是值传递。语言的方法调用只支持参数的值传递。当一个对象实例作为一个参数被传递到方法中时,参数的值訫是对该对象的引用。对象的属性可以在被调用过程中被改变,但对对象引用的改变是不会影响到调用者的。和中可以通过传引用或传输出参数来改变传入的参数的值。在中可以编写如下所示的代码,但是在中却做不到。说明:中没有传引用实在是非常的不方便,这点在中仍然没有得到改进,正是如此在编写的代码中才会出现大量的类(将需要通过方法调用修改的引用置类中,再将对象传入方法),这样的做法只会让代码变得臃肿,尤其是让从和转型为程序员的开发者无法容。和的区别?答:平台提供了两种类型的字符串和,它们可以储存和操作字符串。其中是只读字符串,也就意味着引用的字符串内容是不能被改变的。而类表小的字符串对象可以直接进行修改是中引入的,它和的方法完全相同,区别在于它是在单线程环境下使用的,因为它的所有方面都没有被修饰,因此它的效率也比要高。面试题什么情况下用运算符进行字符串连接比调用对象的方法连接字符串性能更好?如果是少量的字符串拼接,可以用,如果是大量的还是用吧是线程安全的是线程不安全的,很6114明显,的系统开销要大,所以如果我们只有个单线程,考虑速度的话更好。那为什么我们很少见到呢?原因很简单,因为我们有时候很难确定我们创建的系统会不会是多线程的,如果考虑到以后扩展的可能性,则更难确定,所以我们更愿意使用因为它是线程安全的,不用担心以后扩展。面试题请说出下面程序的输出。补充:解答上面的面试题需要清楚两点对象的方法会得到字符串对象在常量池中对应的版本的引用(如果常量池中有一个字符串与对象的结果是),如果常量池中没有对应的字符串,则该字符串将被添加到常量池中,然后返回常量池中字符串的引用;字符串的操作其本质是创建了对象进行操作,然后将拼接后的对象用方法处理成对象,这一点可以用命令获得文件对应的字节码指令就可以看出来。方法就是把该对象放进常量池。、重载()和重写()的区别。重载的方法能否根据返回类型进行区分?答:方法的重载和重写都是实现多态的方式,区别在于前者实现的是编译时的多态性,而后者实现的是运行时的多态性。重载发生在一个类中,同名的方法如果有不同的参数列表(参数类型不同、参数个数不同或者二者都不同)则视为重载;重写发生在了类与父类之间,重写要求子类被重写方法与父类被重写方法有相同的返回类型,比父类被重写方法更好访问,不能比父类被重写方法声明更多的异常(里氏代换原则)。重载对返回类型没有特殊的要求面试题:华为的面试题中曾经问过这样一个问题为什么不能根据返回类型来区分重载,快说出你的答案吧!返回类型不同不构成重载,重载的机制是参数列表不同,即参数的类型,个数,排列顺序。、描述·下加载文件的原理机制?答中类的装载是由类加载器()和它的子类来实现的,中的类加载器是一个重要的运行时系统组件,它负责在运行时查找和装入类文件中的类。由于的跨平台性,经过编译的源程序并不是·个可执行程序,而是个或多个类文件。当程序需要使用某个类时,会确保这个类已经被加载、连接(验证、准备和解析)和初始化。类的加载是指把类的文件中的数据读入到内存中,通常是创建一个字节数组读入文件,然后产生与所加载类对应的对象。加载完成后,对象还不完整,所以此时的类还不可用。当类被加载后就进入连接阶段,这一阶段包括验证7114准备(为静态变量分配内存并设置默认的初始值)和解析(将符号引用替换为直接引用)三个步骤。最后对类进行初始化,包括:如果类存在直接的父类并且这个类还没有被初始化,那么就先初始化父类;如果类中存在初始化语句,就依次执行这些初始化语类的加载是由类加载器完成的,类加载器包括:根加载器()、扩展加载器)、系统加载器()和用户自定义类加载器(的子类)。从)开始,类加载过程采取了父亲委托机制()。更好的保证了平台的安全性,在该机制中自带的是根加载器,其他的加载器都有且仅有一个父类加载器。类的加载首先请求父类加载器加载,父类加载器无能为力时才由其子类加载器自行加载不会向程序提供对的引用。下面是关于几个类加载器的说明:般用本地代码实现,负责加载基础核心类库();从系统属性所指定的目录中加载类库,它的父加载器是又叫应用类加载器,其父类是环境变量或者系统属性所指公应它是应用最广泛的关加载器。它从目录中记载类,是用户自定义加载器的默认父加载器。型变量中能不能存贮一个中文汉字,为什么?答:类型可以存储一个中文汉字,因为中使用的编码是不选择任何特定的编码,直接使用字符在字符集中的编号,这是统一的唯一方法),一个类型占个字节(比特),所以放一个中文是没问题的补充:使用意味着字符在内部和外部有不同的表现形式,在内部都是当这个字符被从内部转移到外部时(例如存入文件系统中),需要进行编码转换。所以中有字节流和字符流,以及在字符流和字节流之间进行转换的转换流,和,这两个类是字节流和字符流之间的适配器类,承担了编码转换的任务;对于程序员来说,要完成这样的编码转换恐怕要依赖于(联合体共用体)共享内存的特征米实现了。、抽象类和接口()有什么异同?答:抽象类和接口都不能够实例化,但可以定义抽象类和接口类型的引用。一个类如果继承」某个抽象类或者实现了某个接口都需要对其中的抽象方法全部进行实现,否则该类仍然需要被声明为抽象类。接口比抽象类更加抽象,因为抽象类中可以定义构造器,可以有抽象方法和具体方法,而接口中不能定义构造器而且其中的方法全部都是抽象方法。抽象类中的成员可以是默认的,而接口中的成员全都是的抽象类中可以定义成员变量,而接∏中定义的成员变量实际上都是常量。有抽象方法的类必须被声明为抽象类,而抽象类未必要有抽象方法、静态嵌套类和内部类()的不同?是被声明为静态)的内部类,它可以不依赖于外部类实例被实例化。而通常的内部类需要在外部类实例化后才能实例化,其语法看起来挺诡异的,如下所示。扑克类(一副扑克)骆昊黑桃红桃草花方块8114构造器洗牌(随机乱序)发牌发牌的位置下片类(一张扑克)内部类骆昊花色点数9114测试代码:汏牌发第一张牌对于非静态内部类只有通过其外部类对象才能创建对象红心自己创建一张牌洗牌后的第一张打印红心面试题下面的代码哪些地方公产生编译错误?注意中非静态内部类对象的创建要依赖其外部类对象,上面的面试题中和方法都是静态方法,静态方法中没有,也就是说没有所谓的外部类对象,因此无法创建内部类对象,如果要在静态方法中创建内部类对象,可以这样做:、中会存在内存泄漏吗,请简单描述答:理论上因为有垃圾回收机制()不会存在内存泄露问题(这也是被广泛使用于服务器端编程的一个重要原因);然而在实际开发中,可能会存在无用但可达的对象,这些对象不能被回收,因此也会导致内存泄露的发生。例如的10/114
- 2020-06-20下载
- 积分：1
