数学研究生教程：非光滑分析和控制论 nonsmooth analysis and control theory

图书标准信息

• 作者 [法]科拉克（Clarke,F.H） 著
• 出版社 世界图书出版公司
• 出版时间 2009-01
• 版次 1
• ISBN 9787506292658
• 定价 39.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 276页
• 正文语种 英语

【内容简介】

　　Nonsmoothanalysisreferstodifferentialanalysisintheabsenceofdifferentiability.Itcanberegardedasasubfieldofthatvastsubjectknownasnonlinearanalysis.Whilenonsmoothanalysishasclassicalroots(weclaimtohavetraceditslineagehacktoDini),itisonlyinthelastdecadesthatthesubjecthasgrownrapidly.Tothepoint,infact,thatfurtherdevelopmenthassometimesappearedindangerofbeingstymied,duetotheplethoraofdefinitionsandunclearlyrelatedtheories.

【目录】

Preface
ListofFigures
0Introduction
1AnalysisWithoutLineaxization
2Flow-InvariantSets
3Optimization
4ControlTheory
5Notation

1ProximalCalculusinHilbertSpace
1ClosestPointsandProximalNormals
2ProximalSubgradients
3TheDensityTheorem
4MinimizationPrinciples
5QuadraticInf-Convolutions
6TheDistanceFunction
7LipschitzFunctions
8TheSumRule
9TheChainRule
10LimitingCalculus
11ProblemsonChapter1

2GeneralizedGradientsinBanachSpace
1DefinitionandBasicProperties
2BasicCalculus
3RelationtoDerivatives
4ConvexandRegularFunctions
5TangentsandNormals
6RelationshiptoProximalAnalysis
7TheBouligandTangentConeandRegularSets
8TheGradientFormulainFiniteDimensions
9ProblemsonChapter2

3SpecialTopics
1ConstrainedOptimizationandValueFunctions
2TheMeanValueInequality
3SolvingEquations
4DerivateCalculusandRademachersTheorem
5SetsinL2andIntegralb-~~nctionals
6TangentsandInteriors
7ProblemsonChapter3

4AShortCourseinControlTheory
1TrajectoriesofDiffercntiMInclusions
2WeakInvariance
3LipschitzDependenceandStrongInvariance
4Equilibria
5LyapounovTheoryandStabilization
6MonotonicityandAttainability
7TheHamiltonJacobiEquationandViscositySolutions
8FeedbackSynthesisfromSemisolutions
9NecessaryConditionsforOptimalControl
10NormalityandControllability
11ProblemsonChapter4
NotesandComments
ListofNotation
Bibliography
Index