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[法] 科拉克 (Clarke,F.H) 著 / 世界图书出版公司 / 2009-01 / 平装
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数学研究生教程:非光滑分析和控制论
Nonsmoothanalysisreferstodifferentialanalysisintheabsenceofdifferentiability.Itcanberegardedasasubfieldofthatvastsubjectknownasnonlinearanalysis.Whilenonsmoothanalysishasclassicalroots(weclaimtohavetraceditslineagehacktoDini),itisonlyinthelastdecadesthatthesubjecthasgrownrapidly.Tothepoint,infact,thatfurtherdevelopmenthassometimesappearedindangerofbeingstymied,duetotheplethoraofdefinitionsandunclearlyrelatedtheories.
PrefaceListofFigures0Introduction1AnalysisWithoutLineaxization2Flow-InvariantSets3Optimization4ControlTheory5Notation1ProximalCalculusinHilbertSpace1ClosestPointsandProximalNormals2ProximalSubgradients3TheDensityTheorem4MinimizationPrinciples5QuadraticInf-Convolutions6TheDistanceFunction7LipschitzFunctions8TheSumRule9TheChainRule10LimitingCalculus11ProblemsonChapter12GeneralizedGradientsinBanachSpace1DefinitionandBasicProperties2BasicCalculus3RelationtoDerivatives4ConvexandRegularFunctions5TangentsandNormals6RelationshiptoProximalAnalysis7TheBouligandTangentConeandRegularSets8TheGradientFormulainFiniteDimensions9ProblemsonChapter23SpecialTopics1ConstrainedOptimizationandValueFunctions2TheMeanValueInequality3SolvingEquations4DerivateCalculusandRademachersTheorem5SetsinL2andIntegralb-~~nctionals6TangentsandInteriors7ProblemsonChapter34AShortCourseinControlTheory1TrajectoriesofDiffercntiMInclusions2WeakInvariance3LipschitzDependenceandStrongInvariance4Equilibria5LyapounovTheoryandStabilization6MonotonicityandAttainability7TheHamiltonJacobiEquationandViscositySolutions8FeedbackSynthesisfromSemisolutions9NecessaryConditionsforOptimalControl10NormalityandControllability11ProblemsonChapter4NotesandCommentsListofNotationBibliographyIndex
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