最优化导论

图书标准信息

• 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
• ISBN 9787115176073
• 定价 59.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 357页
• 字数 418千字
• 正文语种 英语
• 原版书名 A First Course in Optimization Theory
• 丛书 图灵原版数学·统计学系列

【内容简介】

　　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】

　　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】

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