Lectures on Stochastic Programming-Model
这是一本关于随机规划比较全面的书！比较难，不太容易啃，但是读了之后收获很大。这是高清版的！To Julia, Benjamin, Daniel, Nalan, and Yael;to Tsonka Konstatin and Marekand to the memory of feliks, Maria, and dentcho2009/8/20pagContentsList of notationserace1 Stochastic Programming ModelsIntroduction1.2 Invento1.2.1The news vendor problem1.2.2Constraints12.3Multistage modelsMultiproduct assembl1.3.1Two-Stage Model1.3.2Chance Constrained ModeMultistage modelPortfolio selection131.4.1Static model14.2Multistage Portfolio selection14.3Decision rule211.5 Supply Chain Network Design22Exercises2 Two-Stage Problems272.1 Linear Two-Stage Problems2.1.1Basic pi272.1.2The Expected Recourse Cost for Discrete Distributions 302.1.3The Expected Recourse Cost for General Distributions.. 322.1.4Optimality Conditions垂Polyhedral Two-Stage Problems422.2.1General Properties422.2.2Expected recourse CostOptimality conditions2.3 General Two-Stage Problems82.3.1Problem Formulation, Interchangeability482.3.2Convex Two-Stage Problems2.4 Nonanticipativity2009/8/20page villContents2.4.1Scenario formulation2.4.2Dualization of Nonanticipativity Constraints2.4.3Nonanticipativity duality for general Distributions2.4.4Value of perfect infExercises3 Multistage problems3. 1 Problem Formulation633.1.1The general setting3.1The Linear case653.1.3Scenario trees3.1.4Algebraic Formulation of nonanticipativity constraints 7lDuality....763.2.1Convex multistage problems·763.2.2Optimality Conditions3.2.3Dualization of Feasibility Constraints3.2.4Dualization of nonanticipativity ConstraintsExercises4 Optimization models with Probabilistic Constraints874.1 Introduction874.2 Convexity in Probabilistic Optimization4.2Generalized Concavity of Functions and measures4.2.2Convexity of probabilistically constrained sets1064.2.3Connectedness of Probabilistically Constrained Sets... 113Separable probabilistic Constraints.1144.3Continuity and Differentiability Properties ofDistribution functions4.3.2p-Efficient Points.1154.3.3Optimality Conditions and Duality Theory1224 Optimization Problems with Nonseparable Probabilistic Constraints.. 1324.4Differentiability of Probability Functions and OptimalityConditions13344.2Approximations of Nonseparable ProbabilisticConstraints134.5 Semi-infinite Probabilistic Problems144E1505 Statistical Inference155Statistical Properties of Sample Average Approximation Estimators.. 1555.1.1Consistency of SAA estimators1575.1.2Asymptotics of the saa Optimal value1635.1.3Second order asStochastic Programs5.2 Stoch1745.2.1Consistency of solutions of the SAA GeneralizedEquatio1752009/8/20pContents5.2.2Atotics of saa generalized equations estimators 1775.3 Monte Carlo Sampling Methods180Exponential Rates of Convergence and Sample sizeEstimates in the Case of a finite Feasible se1815.3.2Sample size estimates in the General Case1855.3.3Finite Exponential Convergence1915.4 Quasi-Monte Carlo Methods1935.Variance-Reduction Techniques198Latin hmpling1985.5.2Linear Control random variables method200ng and likelihood ratio methods 205.6 Validation analysis5.6.1Estimation of the optimality g2025.6.2Statistical Testing of Optimality Conditions2075.7Constrained Probler5.7.1Monte Carlo Sampling Approach2105.7.2Validation of an Optimal solution5.8 SAA Method Applied to Multistage Stochastic Programmin205.8.1Statistical Properties of Multistage SAA Estimators22l5.8.2Complexity estimates of Multistage Programs2265.9 Stochastic Approximation Method2305.9Classical Approach5.9.2Robust sA approach..23359.3Mirror Descent sa method235.9.4Accuracy Certificates for Mirror Descent Sa Solutions.. 244Exercis6 Risk Averse Optimi2536.1 Introductio6.2 Mean-Risk models.2546.2.1Main ideas of mean -Risk analysis546.2.2Semideviation6.2.3Weighted Mean Deviations from Quantiles.2566.2.4Average value-at-Risk2576.3 Coherent risk measures2616.3.1Differentiability Properties of Risk Measures2656.3.2Examples of risk Measures..2696.3.3Law invariant risk measures and Stochastic orders2796.3.4Relation to Ambiguous Chance Constraints2856.4 Optimization of risk measures.2886.4.1Dualization of Nonanticipativity Constraints2916.4.2Examples...2956.5 Statistical Properties of Risk measures6.5.IAverage value-at-Ris6.52Absolute semideviation risk measure301Von mises statistical functionals3046.6The problem of moments306中2009/8/20page xContents6.7 Multistage Risk Averse Optimization3086.7.1Scenario tree formulation3086.7.2Conditional risk mappings3156.7.3Risk Averse multistage Stochastic Programming318Exercises3287 Background material3337.1 Optimization and Convex Analysis..334Directional Differentiability3347.1.2Elements of Convex Analysis3367.1.3Optimization and duality3397.1.4Optimality Conditions.............3467.1.5Perturbation analysis3517.1.6Epiconvergence3572 Probability3597.2.1Probability spaces and random variables7.2.2Conditional Probability and Conditional Expectation... 36372.3Measurable multifunctions and random functions3657.2.4Expectation Functions.3687.2.5Uniform Laws of Large Numbers...,,3747.2.6Law of Large Numbers for Random Sets andSubdifferentials3797.2.7Delta method7.2.8Exponential Bounds of the Large Deviations Theory3877.2.9Uniform Exponential Bounds7.3 Elements of Functional analysis3997.3Conjugate duality and differentiability.......... 4017.3.2Lattice structure4034058 Bibliographical remarks407Biibliography415Index4312009/8/20pageList of Notationsequal by definition, 333IR", n-dimensional space, 333A, transpose of matrix(vector)A, 3336I, domain of the conjugate of risk mea-C(X) space of continuous functions, 165sure p, 262CK, polar of cone C, 337Cn, the space of nonempty compact sub-C(v,R"), space of continuously differ-sets of r 379entiable mappings,176set of probability density functions,I Fr influence function. 3042L, orthogonal of (linear) space L, 41Sz, set of contact points, 3990(1), generic constant, 188b(k; a, N), cdf of binomial distribution,Op(), term, 382214S, the set of &-optimal solutions of theo, distance generating function, 236true problem, 18g(x), right-hand-side derivative, 297Va(a), Lebesgue measure of set A C RdCl(A), topological closure of set A, 334195conv(C), convex hull of set C, 337W,(U), space of Lipschitz continuousCorr(X, Y), correlation of X and Y 200functions. 166. 353CoV(X, Y, covariance of X and y, 180[a]+=max{a,0},2ga, weighted mean deviation, 256IA(, indicator function of set A, 334Sc(, support function of set C, 337n(n.f. p). space. 399A(x), set ofdist(x, A), distance from point x to set Ae multipliers vectors334348dom f, domain of function f, 333N(μ,∑), nonmal distribution,16Nc, normal cone to set C, 337dom 9, domain of multifunction 9, 365IR, set of extended real numbers. 333o(z), cdf of standard normal distribution,epif, epigraph of function f, 333IIx, metric projection onto set X, 231epiconvergence, 377convergence in distribution, 163SN, the set of optimal solutions of the0(x,h)d order tangent set 348SAA problem. 156AVOR. Average value-at-Risk. 258Sa, the set of 8-optimal solutions of thef, set of probability measures, 306SAA problem. 181ID(A, B), deviation of set A from set Bn,N, optimal value of the Saa problem,334156IDIZ], dispersion measure of random vari-N(x), sample average function, 155able 7. 2541A(, characteristic function of set A, 334吧, expectation,361int(C), interior of set C, 336TH(A, B), Hausdorff distance between setsLa」, integer part of a∈R,219A and B. 334Isc f, lower semicontinuous hull of funcN, set of positive integers, 359tion f, 3332009/8/20pageList of notationsRc, radial cone to set C, 337C, tangent cone to set C, 337V-f(r), Hessian matrix of second orderpartial derivatives, 179a. subdifferential. 338a, Clarke generalized gradient, 336as, epsilon subdifferential, 380pos w, positive hull of matrix W, 29Pr(A), probability of event A, 360ri relative interior. 337upper semideviation, 255Le, lower semideviation, 255@R. Value-at-Risk. 25Var[X], variance of X, 149, optimal value of the true problem, 1565=(51,……,5), history of the process,{a,b},186r, conjugate of function/, 338f(x, d), generalized directional deriva-g(x, h), directional derivative, 334O,(, term, 382p-efficient point, 116lid, independently identically distributed,1562009/8/20page xlllPrefaceThe main topic of this book is optimization problems involving uncertain parametersfor which stochastic models are available. Although many ways have been proposed tomodel uncertain quantities stochastic models have proved their flexibility and usefulnessin diverse areas of science. This is mainly due to solid mathematical foundations andtheoretical richness of the theory of probabilitystochastic processes, and to soundstatistical techniques of using real dataOptimization problems involving stochastic models occur in almost all areas of scienceand engineering, from telecommunication and medicine to finance This stimulates interestin rigorous ways of formulating, analyzing, and solving such problems. Due to the presenceof random parameters in the model, the theory combines concepts of the optimization theory,the theory of probability and statistics, and functional analysis. Moreover, in recent years thetheory and methods of stochastic programming have undergone major advances. all thesefactors motivated us to present in an accessible and rigorous form contemporary models andideas of stochastic programming. We hope that the book will encourage other researchersto apply stochastic programming models and to undertake further studies of this fascinatinand rapidly developing areaWe do not try to provide a comprehensive presentation of all aspects of stochasticprogramming, but we rather concentrate on theoretical foundations and recent advances inselected areas. The book is organized into seven chapters The first chapter addresses modeling issues. The basic concepts, such as recourse actions, chance(probabilistic)constraintsand the nonanticipativity principle, are introduced in the context of specific models. Thediscussion is aimed at providing motivation for the theoretical developments in the book,rather than practical recommendationsChapters 2 and 3 present detailed development of the theory of two-stage and multistage stochastic programming problems. We analyze properties of the models and developoptimality conditions and duality theory in a rather general setting. Our analysis coversgeneral distributions of uncertain parameters and provides special results for discrete distributions, which are relevant for numerical methods. Due to specific properties of two- andmultistage stochastic programming problems, we were able to derive many of these resultswithout resorting to methods of functional analvsisThe basic assumption in the modeling and technical developments is that the proba-bility distribution of the random data is not influenced by our actions(decisions). In someapplications, this assumption could be unjustified. However, dependence of probability dis-tribution on decisions typically destroys the convex structure of the optimization problemsconsidered, and our analysis exploits convexity in a significant way
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Adaptive Filters
自适应滤波器的权威Sayed的大作，用大量的实例诠释自适应滤波器的各种算法原理，是不可多得的好书。ADAPTIVE FILTERSADAPTIVE FILTERSALIH SAYEDUniversity of California at Los Angeles◆旧EEEIEEE PressWIlEYNTERSCIENCEA JOHN WILEY SONS, INC, PUBLICATIONCover design by Michael RutkowskiCopyright C 2008 by John Wiley Sons, Inc. All rights reservedPublished by John Wiley Sons, Inc, Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or bymeans, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under anySection 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of thePublisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center,Inc, 222 Rosewood Drive, Danvers, MA01923, (978)750-8400, fax(978)750-4470, or on the web atwww.copyright.comRequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment, John Wiley sons, Inc, 111 River Street, Hoboken, NJ,(201)748-6011, fax(201)748-6008,oronlineathttp:/www.wiley.com/go/permissionLimit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy or completeness ofe contents of this book and specifically disclaim any implied warranties of merchantability or fitness for aarticular purpose. No warranty may be created or extended by sales representatives or written sales materialsThe advice and strategies contained herein may not be suitable for your situation. You should consult with aprofessional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or anyother commercial damages, including but not limited to special, incidental, consequential, or other damagesFor general information on our other products and services or for technical support, please contact our CustomerCare Department within the United States at(800)762-2974, outside the United States at (317)572-3993 or fax(317)572-4002Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not beavailable in electronic formats. For more information about wiley products, visit our web site atwww.wlley.conLibrary of Congress Cataloging-in-Publication Data:Sayed, Ali hAdaptive filters/Ali H. Sayedp cmIncludes bibliographical references and indexISBN9780470-25388-5( cloth)Adaptive filters. I. TitleTK7872F5s285200862138l5324dc222008003731Printed in the united states of america10987654321To my parentsContentsPrefacexviiNotationXXVAcknowledgmentsXXXBACKGROUND MATERIALA Random variablesA 1 Variance of a random variableA2 Dependent random VariablesA3 Complex-Valued Random VariablesA 4 Vector -Valued Random variables3467A.5 Gaussian Random VectorsB Linear Algebra12B. Hermitian and Positive- Definite matricesB 2 Range spaces and nullspace of matrices14B3 Schur Complements16B 4 Cholesky factorizationB 5 QR DecompositionB6 Singular Value Decomposition20B 7 Kronecker productsC Complex Gradients25C 1 Cauchy-Riemann Conditions5C2 Scalar arguments26C3 Vector arguments26PART:。 PTIMAL ESTIMATIONScalar- Valued Data291. 1 Estimation Without observations1.2 Estimation Given Dependent observations1.3 Orthogonality Principl36CONTENTS1,4 Gaussian random variables382 Vector- Valued Data422. 1 Optimal Estimator in the vector Case422.2 Spherically Invariant Gaussian Variables462. 3 Equivalent Optimization Criterion49Summary and Notes51Problems and Computer Projects54PART I: LINEAR ESTIMATION3 Normal Equatlons603. 1 Mean-Square Error Criterion613.2 Minimization by Differentiation3.3 Minimization by Completion-of-Squares633.4 Minimization of the error Covariance matrix653.5 Optimal Linear estimator4 Orthogonality princlple4. 1 Design Examples4.2 Orthogonality Condition4.3 Existence of solutions744, 4 Nonzero-Mean variables5 Linear Models5.1 Estimation using Linear Relations5.2 Application: Channel Estimation5Application: Block Data Estimation815. 4 Application: Linear Channel equalization825.5 Application: Multiple-Antenna Receivers85Constralned estimation876.1 Minimum-Variance Unbiased estimation6.2 Example: Mean Estimation6.3 Application: Channel and Noise Estimation916.4 Application: Decision Feedback Equalization6.5 Application: Antenna Beamforming1017 Kalman Filter1047.1 Innovations process7.2 State-Space Model106
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