最优化导论
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作者[美]桑达拉姆 著
出版社人民邮电出版社
出版时间2008-04
版次1
装帧平装
上书时间2024-07-03
商品详情
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图书标准信息
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作者
[美]桑达拉姆 著
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出版社
人民邮电出版社
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出版时间
2008-04
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版次
1
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ISBN
9787115176073
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定价
59.00元
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装帧
平装
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开本
16开
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纸张
胶版纸
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页数
357页
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字数
418千字
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正文语种
英语
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原版书名
A First Course in Optimization Theory
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丛书
图灵原版数学·统计学系列
- 【内容简介】
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最优化是在20世纪得到快速发展的一门学科。本书介绍了最优化理论及其在经济学和相关学科中的应用,全书共分三个部分。第一部分研究了Rn中最优化问题的解的存在性以及如何确定这些解,第二部分探讨了最优化问题的解如何随着基本参数的变化而变化,最后一部分描述了有限维和无限维的动态规划。另外,还给出基础知识准备一章和三个附录,使得本书自成体系。
本书适合于高等院校经济学、工商管理、保险学、精算学等专业高年级本科生和研究生参考。
- 【作者简介】
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RangarajanK.Sundaram,毕业于美国康乃尔大学,哲学博士,工商管理硕士。先后在罗切斯特人学和组约人学斯特恩商学院任教,授课课程涉及微分、期权定价、最优化理论、博弈论、公司理财、经济学原理、中级微观经济学和数理经济学等。研究领域包括:代理问题、管理层薪资水平、公司础财、衍生工具定价、信用风险与信用衍生工具等。他在世界顶级学术期刊上还发表了大量论文。
- 【目录】
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MathematicalPreliminaries
1.1NotationandPreliminaryDefinitions
1.1.1Integers,Rationals,Reals,Rn
1.1.2InnerProduct,Norm,Metric
1.2SetsandSequencesinRn
1.2.1 SequencesandLimits
1.2.2SubsequencesandLimitPoints
1.2.3CauchySequencesandCompleteness
1.2.4Suprema,Infima,Maxima,Minima
1.2.5 MonotoneSequencesinR
1.2.6TheLimSupandLimInf
1.2.7OpenBalls,OpenSets,ClosedSets
1.2.8 BoundedSetsandCompactSets
1.2.9ConvexCombinationsandConvexSets
1.2.10Unions,Intersections,andOtherBinaryOperations
1.3Matrices
1.3.1 Sum,Product,Transpose
1.3.2SomeImportantClassesofMatrices
1.3.3RankofaMatrix
1.3.4 TheDeterminant
1.3.5 TheInverse
1.3.6CalculatingtheDeterminant
1.4Functions
1.4.1 ContinuousFunctions
1.4.2DifferentiableandContinuouslyDifferentiableFunctions
1.4.3PartialDerivativesandDifferentiability
1.4.4DirectionalDerivativesandDifferentiability
1.4.5HigherOrderDerivatives
1.5QuadraticForms:DefiniteandSemidefiniteMatrices
1.5.1QuadraticFormsandDefiniteness
1.5.2IdentifyingDefinitenessandSemidefiniteness
1.6SomeImportantResults
1.6.1SeparationTheorems
1.6.2TheIntermediateandMeanValueTheorems
1.6.3TheInverseandImplicitFunctionTheorems
1.7Exercises
2OptimizationinR
2.1OptimizationProblemsinRn
2.2OptimizationProblemsinParametricForm
2.3OptimizationProblems:SomeExamples
2.5ARoadmap
2.6Exercises
3ExistenceofSolutions:TheWeierstrassTheorem
3.1TheWeierstrassTheorem
3.2TheWeierstrassTheoreminApplications
3.3AProofoftheWeierstrassTheorem
3.4Exercises
4UnconstrainedOptima
4.1"Unconstrained"Optima
4.2First-OrderConditions
4.3Second-OrderConditions
4.4UsingtheFirst-andSecond-OrdeiConditions
4.5AProofoftheFirst-OrderConditions
4.6AProofoftheSecond-OrderConditions
4.7Exercises
5EqualityConstraintsandtheTheoremofLagrange
5.1ConstrainedOptimizationProblems
5.2EqualityConstraintsandtheTheoremofLagrange
5.2.1StatementoftheTheorem
5.2.2TheConstraintQualification
5.2.3TheLagrangeanMultipliers
5.3Second-OrderConditions
5.4UsingtheTheoremofLagrange
5.4.1A"Cookbook"Procedure
5.4.2WhytheProcedureUsuallyWorks
5.4.3WhenItCouldFail
5.4.4ANumericalExample
5.5TwoExamplesfromEconomics
5.5.1AnIllustrationfromConsumerTheory
5.5.2AnIllustrationfromProducerTheory
5.5.3Remarks
5.6AProofoftheTheoremofLagrange
5.7AProofoftheSecond-OrderConditions
5.8Exercises
6InequalityConstraintsandtheTheoremofKuhnandTucker
6.1TheTheoremofKuhnandTucker
6.1.1StatementoftheTheorem
6.1.2TheConstraintQualification
6.1.3TheKuhn-TuckerMultipliers
6.2UsingtheTheoremofKuhnandTucker
6.2.1A"Cookbook"Procedure
6.2.2WhytheProcedureUsuallyWorks
6.2.3WhenItCouldFail
6.2.4ANumericalExample
6.3IllustrationsfromEconomics
6.3.1AnIllustrationfromConsumerTheory
6.3.2AnIllustrationfromProducerTheory
6.4TheGeneralCase:MixedConstraints
6.5AProofoftheTheoremofKuhnandTucker
6.6Exercises
7ConvexStructuresinOptimizationTheory
7.1ConvexityDefined
7.1.1ConcaveandConvexFunctions
7.1.2StrictlyConcaveandStrictlyConvexFunctions
7.2ImplicationsofConvexity
7.2.1ConvexityandContinuity
7.2.2ConvexityandDifferentiability
7.2.3ConvexityandthePropertiesoftheDerivative
7.3ConvexityandOptimization
7.3.1SomeGeneralObservations
7.3.2ConvexityandUnconstrainedOptimization
7.3.3ConvexityandtheTheoremofKuhnandTucker
7.4UsingConvexityinOptimization
7.5AProofoftheFirst-DerivativeCharacterizationofConvexity
7.6AProofoftheSecond-DerivativeCharacterizationofConvexity
7.7AProofoftheTheoremofKuhnandTuckerunderConvexity
7.8Exercises
8Quasi-ConvexityandOptimization
8.1Quasi-ConcaveandQuasi-ConvexFunctions
8.2Quasi-ConvexityasaGeneralizationofConvexity
8.3ImplicationsofQuasi-Convexity
8.4Quasi-ConvexityandOptimization
8.5UsingQuasi-ConvexityinOptimizationProblems
8.6AProofoftheFirst-DerivativeCharacterizationofQuasi-Convexity
8.7AProofoftheSecond-DerivativeCharacterizationof
Quasi-Convexity
8.8AProofoftheTheoremofKuhnandTuckerunderQuasi-Convexity
8.9Exercises
9ParametricContinuity:TheMaximumTheorem
10SupermodularityandParametricMonotomicity
11Finite-HorizonDynamicProgramming
12StationaryDiscountedDynamicProgramming
AppendixASetTheoryandLogic:AnIntroduction
AppendixBTheRealLine
Bibliography
Index
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