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
- 2020-12-09下载
- 积分:1
车载智能计算平台白皮书(自动驾驶)
车载智能计算平台白皮书(自动驾驶)版权声明本白皮书版权属于中国软件评测中心,并受法律保护。转载、摘编或利用其它方式使用本白皮书文字或者观点的,应注明“来源:中国软件评测中心”。违反上述声明者,本单位将追究其相关法律责任目录、编制概要(一)编制背景二)编制目标三)编制方法四)特别声明车载智能计算平台内涵与范畴(一)自动驾驶技术目前存在三种发展路线二)汽车智能计算平台包括“车、云、网、库”三)车载智能计算平台是。级及以上自动驾驶的必要解决方案(四)车载智能计算平合的功能定位、车载智能计算平台关键技术发展现状(一)芯片由通用走向专用,类脑芯片提供全新架构二)车载智能计算平台操作系统功能需求不断细化成为主流软件架构三)车载以太网受到广泛关注和进入竞争关键期(四)实现实时动态高精度定位需多技术融合(五)安全需求不断拓展,预期功能安全备受关注(六)测试需求不断细化,车载智能计算平台测试标准尚未形成四、车载智能计算平台相关产业发展现状(一)国内外企业纷纷布局车载智能计算平台(二)互联网企业、整车厂与半导体企业积极布局芯片领域三)车控操作系统国外占据发展先机,开源操作系统或成最大赢家四)国内外汽车网络通信技术产业蓬勃发展(五)“集中众包”成为高精度地图制图新模式五、车载智能计算平台发展现状国内外对比)车载智能计算平台性能方面国外处于领先地位二)国外部分计算平台已实现量产、国内计算平台仍处于样机阶段三)忐片性能方面国内典型产品存在优势六、车载智能计算平台中长期发展趋势(一)自主式和网联式协同推进自动驾驶发展二)电子信息、通信技术与汽车多产业交叉愈加突显三)软硬件协同开发提高车载智能计算平合的综合效率(四)高度集成是未来车载智能计算平台的发展方向五)多种数据处理模式并存的现状仍将持续七、推动车载智能计算平台发展的措施建议(一)明确发展方向前瞻规划布局(二)建立专项基金培育创新能力(三)夯实产业基础完善产业结构四)对外开放交流加强国际合作附件:缩略语、编制概要(一)编制背景汽车工业是中国产业发展的重要驱动。中国汽车工业经过近年的发展,年汽车工业总产值占全国工业总产值的比重达到%,占全国的比重达%。中国汽车市场目前已是全球最大单体汽车市场,年产销量分别占世界汽车产销量的%和%,但千人汽车保有量仅为世界平均值的%,发展空间较大。随着汽车智能化、网联化、电动化和共享化的发展,汽车产业发展面临新一轮的变革机遇,我国应该加大投入,抓住机遇,加快推进汽车强国建设。智能网联汽车从交通运输工具日益转变为新型移动智能终端。汽车功能和属性的改变导致其电子电气架构随之改变,进而需要更强的计算、数据存储和通信能力作为基础,车载智能计算平台是满足上述要求的重要解决方案。作为汽车的“大脑”,车载智能计算平台是新型汽车电子电气架构的核心,也是新犁智能汽车电子产业竞争的主战场明确车载智能计算平合的定义和范畴、关键技术、产业现状以及发展路线,在此基础之上为车载智能计算平台关键技术进步和产业化应用推广提供措施建议,对推动我国智能网联汽车产业持续健康快速发展具有重要意义。《中国公路学报》编辑部口国汽车工稈学术研究综述中国公路学报(二)编制目标通过明确车载智能计算平台的内涵与范畴,界定汽车智能计算平台基本架构和车载智能计算平台功能定位。研究车载智能计算平台的技术框架,梳理车载智能计算平台的关键技术。探索车载智能计算平合相关产业组成,分析车载智能计算平合的产业链结构,研判产业发展趋势。旨在提出促进车载智能计算平台相关技术及产业发展的可行性措施建议,为行业主管部门提供决策参考,为行业健康有序发展提供指导依据(三)编制方法是研究学习国内外相关政策文献,充分借鉴参考国内外主要研究动态和成果。是调研国内外知名车载智能计算平台相关企业,汇集整理和分析来自实践应用的相关素材。三是邀请行业专家咨询评审。(四)特别声明研究范围聚焦技术和产业发展车载智能计算平台将涉及法律、道德、伦理、文化等诸多领域。本白皮书的编制主要是为了给相关行业主管部门和企业提供决策参考依据,集中在技术和产业两大层面展开研究,暂未涉及其他方面。研究内容仍有待进一步丰富完善本白皮书的主要观点和内容仅代表编制组目前对车载智能计算平台的研判和思考,欢迎各方专家学者和企业代表提出宝贵意见,共同推动白皮书的及时更新和纠偏。本白皮书为《车载智能计算平合白皮书(年)》,后续中国软件评测中心将会继续推出《汽车智能计算平台白皮书(系列)。二、车载智能计算平台内涵与范畴(一)自动驾驶技术目前存在三种发展路线年(国际汽车工程师协会)发布《标准道路机动车驾驶自动化系统分类和定义》,并于年月对标准进行了修订更新。标准将自动驾驶分为共个级别。人工驾驶(),即完全由驾驶员执行全部动态驾驶任务(),包括有主动安全系统介入的情况。辅助驾驶(),即由自动驾驶系统在连续的特定设计运行工况(下执行动态驾驶任务的横向或纵向车辆运动控制子任务(但不能同时),并由驾驶员负责完成动态驾驶任务的其余内容。部分自动驾驶(),即由自动驾驶系统在连续的特定设计运行工况下执行动态驾驶任务的横向和纵向车辆运动控制子任务,并由驾驶员负责完成驾驶环境监控,并对道路目标和状态做岀有效回应。条件自动驾驶(),即由自动驾驶系统在连续的特定设计运行工况下执行所有动态驾驶任务。但是要求驾驶员具备汽车功能保障意识,并随时可以对自动驾驶系统发布的干预请求,以及与动态驾驶任务相关的其他车辆系统的故障做出有效回应。高度自动驾驶(),即自动驾驶系统在连续的特定设计运行工况下执行全部动态驾驶任务和功能保障,不要求任何用户对干预请求做出回应。完全自动驾驶(),即由自动驾驶系统在任意连续的运行环境下,执行全部动态驾驶任务和功能保障,不要求任何用户对自动驾驶系统的干颈请求做出回应。
- 2020-12-04下载
- 积分:1