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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鸡啄米VS2010-MFC编程入门教程
鸡啄米的这套VS2010/MFC编程入门教程到此就全部完成了，虽然有些内容还未涉及到，但帮助大家进行VS2010/MFC的入门学习业已足够。以此教程的知识为基础，学习VS2010/MFC较为深入的内容已非难事。作为本教程的最后一课，鸡啄米将对前面所讲内容进行目录归纳，并对这八个月加班加点的努力进行总结。vS2 DIO/MFC编程入门教程之目录和总结-敦一开发-鸡啄米每布课的写作耗时差不多都在两三个小时以上,有时侯甚全写到凌晨一点多。付出了很多,同样也收获了很多,最大的收获莫过于大家的肯定和支,很多朋友都韶言或者发郎件支持鸡啄米,这说明我的辛勤劳动没有白费,帮助了很多人,感谢那些一直以来支关注鸡啄米的朋友,也特别感谢那些在鸡啄米经常留言支持的读者除了大家的支持,鸡啄米自己也通过本教程的完成更深入的理解了的很多内容,提高了对的认认水平,尤其是更加巩了一些较少使用的知认。在帮人的同时也帮了自己很多朋友在鸡啄米留言或者给鸡啄米发电子邮件讨论问题,由时间确实比较少,晚上夏新文章,白天上班,所以只叵复了一部分,望大家见谅。学会了编程,很多人就开始喜欢硏究了,但是提醒大家不要忘了根本,即谙言。从《鸡啄米编程入门系列》和《编程入门教程》这套学习教程的受欢迎程度,鸡啄米感觉大家有些忽规的学习,更喜欢应用性强的在你能熟练使用后,最好再认真学学,提高水平才能真正亡你的编程功力上一个台阶。以后鸡啄米会铼续分亨各种编程知识,还会编写一些教程,希曌人家能一如既往约关注鸡啄米网站,支持鸡啄米!格力高百力漆清风原木纯品系列了!这一耙已有微虾味)*1盒3层谜你纸手帕“10包已D体被害送出兔费领』兔费领推您可能也喜欢:日分2编程入门编稈入编稈入编程入编程入之三应用门之三十九(文档、门之十三(常门之刀十六常门之一五(对话框程序工程中文件的组视图和框架:概述)用类类月类异常处一股属性页对话框的成结构)创建及显示)除非特别注明,鸡啄兴文章均为原创转载请标明本文地止作着鸡啄米分类软件开发浏览评论上一篇:互联网的轻时代已成为趋势下一篇:最全面详细的评测相关文章编程入门之五十四界Ⅲ开发:使用更多空件并为控科添加消息欠理凶数)编程入门之五|三(界面开发:为添加控件)编程入门之开十二(界Ⅲ开发:创建样式的应用程序框架)编程入门之五十一(图形图像:对象之画刷编程入门之五十(图形图像:对象之画笔编程入门之四|元(图形图像:类及其屏暮绘图函数)编程入门之四十八(字体朴文本输出:文输出)编程入门之四十七(字体和文本输出:字体类)编程入门之四十六(常用类:异常处理)http://www.jizhuomi.com/software/257.tml[2013,969:48:41]vS2 DIO/MFC编程入门教程之目录和总结-敦一开发-鸡啄米编程入门之四十五(常用类文件操作类)楼我的名字叫麒我一直自学编程,觉得它比别的都好回复该留言楼愚人笔记希望还有下一个系列面世66鸡啄米于回复嗯,会有的,呵呵回复该留言楼蛉啊了非常感谢!继续加油!回复该留言偻楼主好热心好感动啊写了这么多而且写的非常详细!!再次谢谢你们。。虽然今天查百度无意间点到这里的,不过攸货确实好多,记住鸡啄米了哈!!!。。祝你们网站越来越火哈,,以后我会经常来你们网站的哈哈≤6鸡啄米于回复志同道合的朋友越来越多了回复该留言楼学土之爱楼主了不起啊回复该留言楼求助救助:按你第课制作的计算器,我加入了一个减法功能,里面参数如下初始时刻三个变量对立的都是,我需要他们为空也就是什么都没有还有就是输入数据后或没入数据而按时程序会自动结束,改怎么办?≤鸡啄米于回复变量是存到内存中的,它是不可能为空的,即使你没有赋初值,它也会有初值。按回车退出一般是因为默认按紐是,取消默认按钮或者把中的注掉就行了求助于回复谢谢老师,问题我已经解决了回复该留言楼李志红博客反正不懂这个,米看看。回复该留言http://www.jizhuomi.com/software/257.tml[2013,969:48:41]vS2 DIO/MFC编程入门教程之目录和总结-敦一开发-鸡啄米楼点点滴滴写得非常好,加油回复该留言楼欲取消子节点缩进您好,米哥,我想取消子节点与父节点的缩进,请问应该如何做啊!谢谢啊由鸡啄米于最后编辑回复该留言楼迷哎呀不得了,最近车学回复该留言写的真的非常详细,非常好!!!!怒赞于回复喽主虽是写技术博客,可惜一点讨论的氛围都没有,都是一些菜鸟在这淫须马,博客的板式中也只有喜欢和推两^能,连反对的机会都不给,可见作者多么自恋和自大。让人匪所思!写博客不是为了技术探讨,这种浅尝揶止的文章不如不看!写出来的东西也是玩具,实际立用中很容易腐烂。回复该留言第一次发现这个好东西,顶起,写得真好。回复该留言楼楼主好热心力能的热心楼主啊!!里加入控件怎么加啊????百度半大了也摆不到66喽主好热心于回复楼主快出现呀6鸡啄米于回复,日前还没用过控件,建议再搜索下,网上应该有相关资料回复该留言楼我考研的目的有点像博主,但我是因为自已出太真心没实力的说。。学的不是亡算机,本科也是浑浑噩噩的过去,化了点时间去考研,刚第一个学期,日子依旧浑浑噩噩的,因为要上程序课偶然发现这个对站。。看了博工一番感概,觉得自己确实要给自己一^定位一个方叵,但是我这专业有时候确实让人很迷茫。。。而且现在做什么都克制不住白三可以花上一天的时间看美剧。。。ε最近一直在想我到底该怎么做是好鸡啄米于回复想做什么一定要下决心,尤其是学生阶段,不要到找工作的时侯再着急回复该留言最近在学习很高兴能参照着博主的资料,一步一步一点点的学习下去。对于一个白来说是很好的入门学习材料。希望自己能在本门底将搞定,吼吼。再次感谢博主!!!http://www.jizhuomi.com/software/257.tml[2013,969:48:41]vS2 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