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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田口方法实战技术
田口方法是一种在产品开发和产品设计早起阶段防止质量问题的技术,是一种新颖、科学、有效的质量工程优化设计方法。田口方法以最迅速、最经济的试验方法直交表),使系统在不增加成本情况下,突破设计瓶颈或改善生产制造流程,应用于技术开发、产品开发,能发挥立即有效的成果。前言前言当下竞争国际化与需求多样化的制造业,其产品寿命周期日益缩短,制造厂家惟有用极短的研发周期源源不断地推出新产品,才能在市场上占据有利地位,否则就有失去审场份额的危杌。因为无论多妤的产品,错过了上市时机就可能变得一钱不值!然而即使研发人员加班加点也无济于事,似乎缩短研发周期的潜力已经被挖尽了。事实上只有不断改革“研发方法”才能解决根本问题。田口方法( Taguchi Methods)作为一种非常实用的技术开发、制程改善工具,协助企业快速找出制程环境的最适生产条件,并有效节省产品设计开发时间,而广受研究单位、生产、制程部门的欢迎与肯定。在日本的电子、汽车等行业,应用田口方法被认为是“天经地义的事”。近几年风靡仝球企业的6设计,实际上就是以田口方法为核心的设计,6设计及田口方法在制造业的广泛应用已收到显著效果。田口方法在研发领域更是受到高度评价,被当作是将研发周期编短一半的法宝。本书主要采用循序渐进、由浅入深的系统化方式,倚惜作者30多年来研究实验计划、直交表”的丰富实务体验,从管理的视角阐述了田口方法知识体系的精髓,讲解此套品质工程技术,让初学者和有经验人士皆能建立完整的理念体系,轻而易举地应用于实务工作中。书中包含了田口知识体系中的重要内容,揭示了实际操作中所遇到的各种疑难问题和相应的解决方案。本书在编写过程中,乘持全面、简单、实用的原则,突出以下三个重点1.理论和实践的完美结合。本书从实例出发,导出田口方法深奥的理论,并用众多实倒来解析田口方法的实际应用,为企业高效实施田口方法指明了方向。2.理论全面,重点突出。本书从田口方法理论中的两个重点(比和直交表)出发,全面展开,多方位阐述田口方法的深奥理论。对于研究田口方法的有?田口方法实战技术心人士来说,不愧为一本不可多得的教材。3.化复杂为简单。田口方法深奥的理论,一直困惑着田口方法在实际生产中的应用。本书利用各种图表、各个行业的实例来阐明田口方法深奥的理论,使读者能够从简单到深入,由浅而深,从而理解田口方法的真义。在本书编写过程中,得到了众多企业高层主管、研发、设计、生技、制造、品管人员提供的许多企业实务经验,让本书的实例得以丰富,在此表示感谢。另也感谢本公司同仁李联伟先生协助本人整理多年来积的教材资料与案例,海天出版社相关编辑人员给予的建议,在此一并向他们致以最衷心的感谢及最诚挚的祝福!感谢给我帮助的各个公司,因篇幅有限,未能一一列出(以公司第一字笔画为序排名)六和机械集团友达光电(苏州)有限公司华映光电企业集团光宝电子(东莞)有限公司沪士电子(昆山)有限公司明硕计算机(苏州)有限公司美齐科技股份有限公司信泰联光学(东莞)有限公司润泰企业集团高刨(苏州)电子有限公司捷安特(巨大机械)企业集团舒电子(东莞)有限公司富士康企业集团锦和科技股份有限公司沪士电子董事长吴礼淦先生、捷安特总经理郑宝堂先生,在日理万机之中仍不忘关注抽作的印行,不吝为拙作慨然赐序,其九鼎之言,使本书蓬草生辉,于此谨表哀心的谢忱。林秀雄2004年8月序一序当今企业面对国际化市场竞争及多样化需求,产品/技术市场寿命周期愈益缩短,产品的质量要來越来越严格,惟有用极短的研发周期源源不断地推陈出新,用最稳健的制程参数来控制产品生产流程,才能在市场中占据有利地位。否则企业即会失去市场份颛,在市场竞争中被淘汰。新技术研发(制程条件控制与稳定性解析、新产品与新制程开发)和缩减成本已经成为当前企业经营刻不容缓的深题。自日本著名质量管理专家田口玄一博士在20世纪70年代初创立“田口方法( Taguchi Methods)”以来,田口方法在全世界颇受产业界欢迎,并被迅速推广普及,其提升研发效率及改善品质成效之卓著,影响之深远,更一致受到高度评价。田口方法是一种在产品开发和产品设计早期阶段防止质量问题的技术,是种新颖、科学、有效的质量工程优化设计方法。田口方法以最迅速、最经济的实验方法(直交表),使系统(产品设计或制程改善)在不增加成本(葚至降低成本〕情况下,突破设计瓶颈或改善生产制造流程,应用于技术开发、产品开发能发挥立即有效的成果。近几年全球企业热摔的6设计,实际上就是以田口方法为核心的设计,可见田口方法之实祧,势在必得。捷安特通过30余年来在国际审场的持续精耕,秉持“生活可以更美圩!”的品牌精神,才有了今日之绩效。在充满机遢的全新时代,捷安特以科技、时尚、人性为主题,将人类对于未来的执着和对生活的热爱汇入自行车的设计理念中,维系自然和人的交流,为美好生活创建更完善的产品,这是人类对于未来的理想,也是捷安特对于生活的憧憬。“创新价值,领导流行”,才可以在当今市场竞争中立于不败。在这些成就背后,田口方法在捷安特之推行实施作用重大。↓田口方法奥战技木林秀雄教授,潜心致力于田口方法研究多年,其理论功底之深厚,实践经验之丰富,实属品管界之泰斗,我司有幸邀请林教授莅临,亲自讲授田口方法真义,林教授深入浅出的概念讲解,生动详实的案例分析,强有力地推动了我司田口方法的普及与发展,对我司的可持续发展助意甚大。林教授汇集多年之精湛理论与实践为一炉,与时俱进,编著《田口方法实战技术》一书,本人深感此书内容之前瞻性、实用性。相信此书的面世,将对田口方法在祖国大陆的推广普及,必有实质的作用。特写此一序,郑重推荐之。捷安特(中国)有限公司总经理郑宝堂它孛序二序企业经营者一向是社会经济变化的敏锐唤觉者,更是最务实的执行者面对当今惊涛骇浪的外部市场环境,产品的更新换代步伐加快,消费者对产品的质量要求日益苛刻,如何提高产品的可靠度?如何缩短产品的研发过程?已成为经营者的关注焦点。二次世界大战后,日本工业迅速崛起,他们依靠神秘武器—田口方法,在世界各国市场上大获全胜。在20世纪80年代,田口方法就已在美国囚防、汽车工业领域闻名遐迩。在日本电子、汽车等行业,应用田口方法被认为是“天经地义的事”。可见在企业里推动此方法势在必行。田口玄一博士是著名的质量专家,他以预防为主、正本清源的哲学思想,把數理统计、经济学应用到品质管制工程中,发展出独特的质量控制技术——田口方法。它摒弃了传统的质量观念,提出了新的质量概念,即质量不是靠检验得来的,也不是靠控制生产过程得来的;质量,就是把顾客的质量要求分解转化为设计参数,形成预期目标值,最终生产出低成本且性能稳定可靠的“物美价康”的产品。田口方法作为实验设计的方法,旨在帮助我们用较少的实验次敷,得到与全方位实验同样有效的实验结果,编短研发和技术苹新周期,以最经济的手段改进工艺。该理论以最迅速、最经济的实验方法使产品设计或制程改善在不增加成本(甚至降低成本)情况下,突破设计瓶颈或改善生产制程,应用于技术开发、产品开发中,发挥立即有效的成果。可见田口方法不失为一个简单、科学的方法。学会它,对事件分析处理之能力提升帮助甚大。我司为能聘请林秀雄教授前来讲授田口方法深感荣幸。林教授以多年的实践口方法臭战拉术经验和深厚的理论知识,深入浅出的教导,让学员耳目一新,不再被深奥理论所吓倒。使学员能够切实理解田口方法的真义,在今后的工作中可以将田口方法落到实处,从而为企业的发展带来最大化的效益。此次喜闻林教授即将出版《田口方法实战技术》一书,即满怀期待。现读罢此书,深感此书抛开高深的理论和繁杂的公式,而从众多实例出发,详述田口方法之应用,可谓化繁杂为简单。深信此书的出版将促进田口方法在业界的高效实施,对业界可谓贡献甚大。在此,秉持“知识你我共享”的心情,拙笔一序,希望此书的面世,可以让各行各业的更多朋友了解田口方法,并以此方法来为中国产业界更好地服务!沪士电子股份有限公司董事长吴礼淦4目录目录第一章田口方法与品质工程原理………1)§1.1前言§1.2田口的哲学观念及田口方法…………………(2)§13参数的分类……(3)8I.4品质工程原理(6)§1.5品质管制在各阶段屮的要务9第二章品质损失函数…(13)82.1品质、成本与低成本品质工程观念的启发……………………(13)822工程设计、工程规格与实验计划…………(15)23直交表与实验计划(16)824对数、指数的说明与启发…………(16)§2.5品质损失函数…·●·鲁……·(18)826二次方程式品质损失函数………(21)§27平均品质损失命◆·(25)第三章直交表与应用实例研究…(29)§3.1定义:直交与直交原理………………(29)§3.2直交表的直交性证明………(30)§3.3直交表的使用…………………………(36)?田口力法实战技木第四章实验计划与制程改善模式·◆··;◆···◆··自····◆吉····4····日◆·晋··。···日·●39)§4.1实验计划的目的与主要构成项目……………(39)S4.2应用直交表的实验说明(40)§4.3直交表解析与实验指示说明………(42)§4.4主效果与交互作用的计算与说明§4.5重要因果图解分析、可控制项目、实验指示书与制程改善模式…………(46)第五章品质计量法基础……………………………………………………………(50)§5.1品质管理的发展…………………(50§52品质计量法……………………(52)§5.3举例分析…▲画血最口●看D●曲鲁d…(53)§54三种品质计量方法之比较■■▲·血d自■··晶自看着自垂·自(56)第六章田口方法的运用步骤与著名案例…….(58)S6.1口口方法的运用步骤…………(58)S6.2田口博士著名案例—磁砖制程设计●會●。●鲁·(60)S6.3变异数分析( Analysis of Variance)曹自晋非鲁會●鲁曹●q鲁◆自◆●香鲁↓看§64新旧田口方法的对比……………………………(69)第七章SN比与品质特性基础(73)§7.1SN比的概念和定义公式(73)§7.2田口方法中的静态特性………(75)§7.3田口方法中的动态特性(83)§7.4举例解析甲电自(86)第八章应用直交表的矩阵实验…(0)§81矩阵实验…§8.2因素效应的估量(112)
- 2020-12-11下载
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