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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西门子S7-1200 SCL编程指令手册.pdf
西门子1200PLC SCL编程指令手册,详细介绍西直门1200和1500PLC的SCL编程指令R_TRG检测信号上升沿(S7-1200,S7-1500)RTR|G:检测信号上升沿唱圆说明使用检测信号上升沿”指爷,可以检测输入CLK的从“0"到“1”的状态变化。该指合捋输入CLK的当前值与保存在指定实例中的上次查询(边沿存储位)的状态进行比较。如果该指合检测到输入CLK的状态从“03变成了“1”,就会在输出Q中生成一个信号上升沿,输出的值将为TRUE或“1”一个周期。在其它任何情况下,该指合输出的信号状态均为“0”。烀该指合插入程序中时,烀自动打开“调用选项" Call options)对话框。在该对话框中,可以指定将边沿存储位存储在自身数据块中(单背景)或者作为局部变量存储在块接口中(多重背景)。语法“检测信号上升沿”指爷的语法如下所示(CLK:=参数下表列出了“检测信号上升沿”指爷的参数:参数声明数据类型存储区说明CLKInputBOOL、Q、M、D、L|到达信号,查询该信号的边QOutputBOOL1、Q、MAD、L边沿检测的结果示例以下示例说明了该指合的工作原理SCLR TRIG DB"(CLK : -TagIn>Tagout)i输入CLK中变量的上一个状态存储在“ R TRIG DB”变量中。如果在操作数Tagn1和"Tagn2”或在操作数“Tagn3中检测到信号状态从“0变为“1”,则输出“ Tagout_Q的信号状态为“”一个周期。3F_TRG:检测信号下降沿(S7-1200,S7-1500)FTRG检测信号下降沿唱圆说明使用检测信号下降沿”指爷,可以检测输入CLK的从“1”到"0”的状态变化。该指合捋输入CLK的当前值与保存在指定实例中的上次查询(边沿存储位)的状态进行比较。如果该指合检测到输入CLK的状态从“1"变成了“0,就会在输出Q中生成一个信号下降沿,即输出的值烀为TRUE或“1”一个周期。在其它任何情况下,该指合输出的信号状态均为“0”。烀该指合插入程序中时,烀自动打开“调用选项" Call options)对话框。在该对话框中,可以指定将边沿存储位存储在自身数据块中(单背景)或者作为局部变量存储在块接口中(多重背景)。语法“检测信号下降沿”指爷的语法如下所示(CLK:=参数下表列出了“检测信号下降沿指合的参数:参数声明数据类型存储区说明CLKInputBOOLQ,M、D、L到达信号,查询该信号的边沿QOutputBOOLQ、M、D、L|边沿检测的结果示例以下示例说明了该指合的工作原理SCLF TRIG DB(CLK :TagIn2 =>Tagout)输入CLK中变量的上一个状态存储在“FTRG_DB"变量中。如果检测到操作数“Tagn"的信号状态从“1变为“0”,则输出" Tagout"的信号状态为“1"4定时器操作(S7-1200,S7-1500)定时器操作该章节包括以下主题的信息:TP:生成脉冲S7-1200,S7-1500)TON:接通延时(S7-1200S7-1500ToF∴关断延时(S7-1200,S7-1500)●TONR:时间累加器(S7-1200,S7-1500)RESET TIMER:复位定时器(S7-1200,S7-1500)PRESET TIMER:加戟持续时间(S7-1200,S7-1500)°传统(S7-15005TP:生成脉冲(S7-1200,S7-1500)TP:生成脉冲唱圆说明使用“生成脉冲”指合来设置持续时间PT的参数Q。当参数|N的逻辑运算结果(RLO)从0变为“1”(信号上升沿)时,启动该指合。指合启动时,预设的时间PT即开始计时。随后无论输入信号如何改变都会将参数Q设置为时间PT。如果持续时间PT仍在计时,即使检测到新的上升沿,参数Q的信号状态也不会受到影响。可通过ET参数查询当前的时间值。该时间值从T#0s开始,在达到持续时间PT后结束。达到持续时间PT时,且参数|N的信号状态为“0”,则复位参数ET。说明如果程序中未调用定时器(这是因为会忽略定时器),则输出ET会在定时器计时结束后立即返回个常数值。每次调用“生成脉冲指合,都会为其分配一个G定时器用于存储指合数据。对于S7-1200cPUEC定时器是一个 C TIMER或 TP TIME数据类型的结构,可如下声明声明为一个系统数据类型为|C_TMER的数据块(例如,MyEC_TMER●声明为块中“ Static程序段内类型为 TP TIME的局部变量(例如,# MyTP_TIMER)对于S7-1500cPUEC定时器是一个 C TIMER、旧 C LTIMER、 TP TIME或 TP LTIME数据类型的结构,可如下声明声明为一个系统数据类型为 C TIMER或lC_ LTIMER的数据块(例如," MylEC_TIMER”)声明为块中 Static部分的 TP TIME或 TP LTIME类型的局部变量(例如,# MyTP_ TIMER)在程序中插入该指合时,将打开“调用选项” Call options)对话框,可以指定C定时器将存储在自身数据块中(单个背景)或者作为局部变量存储在块接口中(多重背景如果创建了一个单独的数据块则该数据块捋保存到项目树“程序块>系统块"( Program blocks> System blocks)路径中的“程序资源( Program resources)文件夹内。有关本主题的更多信息,请参见“另请参见"。只有在调用该指合且每次都会访问Q或ET输出时,才会更新指爷数据。语法生成脉冲”指合的语法如下所示●系统数据类型为EC_ Timer的数据块(全局DB)SCLTP(IN:=PT:=ET=>●局部变量TP:生成脉冲(S7-1200,87-1500)SCLmoloc1 timer(工NPT:=rQ=>)该指合的语法由以下部分组成参数声明数据类型存储区说明s7-1200S7-1500NBOOLBOOL.M.D.|启动输及脉冲的持续时PTIniTIMETIMEl、Q、M、D、间。LTIMEPT参数的值必须为正数OutputBOOLBOOLQ、M、D、在PT持续时间内保持置位状态的操作数TIMEETOutputMEl、Q、M、DLTIME当前时间值有关有效数据类型的更多信息,请参见“另请参见"。脉冲时序图下图显示了“生成脉冲”指合的脉冲时序图PTPTPTET示例7TP:生成脉冲(S7-1200,S7-1500)以下示例说明了该指爷的工作原理SCLTP DB".TP(IN Tag start,PT :=Tag PresetTime"Tag statusET =>"Tag ElapsedTime")i当“ Tag_ start"操作数的信号状态从“0”变为“1"时,PT参数预设的时间段开始计时,同时"Tag_ Status"操作数置位为“1”。当前时间值存储在 Tag_ ElapsedTime"操作数中8TON:接通延时(S7-1200,S7-1500)TON:接通延时唱圆说明可以使用接通延时”指合捋Q参数的设置延时PT指定的一段时间。当参数N的逻辑运算结果(RLO从“0变为“1”(信号上升沿)时,启动该指合。指合启动时,预设的时间PT即开始计时。超过持续时间PT时,参数Q的信号状态变为“1。只要启动输入仍为“1”,参数Q就保持置位。如果|N参数的信号状态从“1变为"0”,则复位参数Q。当在参数N上检测到一个新的信号上升沿时,将重新启动定时器功能。可通过ET参数查询当前的时间值。该时间值从T#0s开始,在达到持续时间PT后结束。只要参数N的信号状态变为0”,就立即复位ET参数。说明如果程序中未调用定时器(这是因为会忽略定时器),则输出ET会在定时器计时结束后立即返回一个常数值。每次调用“接通延时指合,必须捋其分配给存储指合数据的EC定时器对于S7-1200CPUEC定时器是一个 C TIMER或 TON TIME数据类型的结构,可如下声明●声明为一个系统数据类型为 C TIMER的数据块(例如, MylEC_ TIMER”)●声明为块中“ Static"程序段内类型为 TON TIME的局部变量(例如,# MyTON_TIMER)对于S71500cPUEC定时器是一个|EC_TMER、 EC LTIMER、TON_TME或 TON LTIME数据类型的结构,可如下声明●声明为一个系统数据类型为旧EC_ TIMER或C_ LTIMER的数据块(例如," MylEC_TIMER")声明为块中“ Static"部分的 TON TIME或 TON LTIME类型的局部变量(例如,# My TON_ TIMER)在程序中插入该指合时,捋打开“调用选项( Call options)对话框,可以指定C定时器烀存储在白身数据块中(单个背景)或者作为局部变量存储在块接口中(多重背景)。如果创建了一个单独的数据块,则该数据块捋保存到项目树“程序块>系统块( Program blocks> System blocks)路径中的“程序资源Program resources)文件夹内。有关本主题的更多信息,请参见“另请参见”。只有在调用该指合且每次都会访问Q或ET输出时,才会更新指合数据。语法接通延时指合的语法如下所示●系统数据类型为C_Tmer的数据块(全局DB)SCLTON(N:=PT:=,Q=>,三=>)9TON:接通延时(S7-1200,S7-1500)●局部变量SCLmoloc1 timer(工N:=rPT:=rQ=>ET)该指合的语法由以下部分组成参数声明数据类型存储区说明s7-1200s7-1500NInputBOOLBOOLl、Q、M、D启动输入接通延时的持TIME、Q、M、D、续时间PTInputTIMELTIMEPT参数的值必须为正数定时器PT内时OutputBOOLQ、M、D、间用完时,保持BOOL置位状态的操作数。TIMETIMEQ、M、DETOutputLTIME当前时间值有关有效数据类型的更多信息,请参见“另请参见”。脉冲时序图下图显示了“接通延时指合的脉冲时序图PTET
- 2020-12-03下载
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