凸分析基础

图书标准信息

• 作者 Jean-Baptiste、Claude Lemarechal 编
• 出版社 世界图书出版公司
• 出版时间 2004-04
• 版次 1
• ISBN 9787506266178
• 定价 38.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 259页

【内容简介】

Thisbookisanabridgedversionofourtwo-volumeopusConvexAnalysisandMinimizationAlgorithms[18],aboutwhichwehavereceivedverypositivefeedbackfromusers,readers,lecturerseversinceitwaspublished-bySpringer-Verlagin1993.Itspedagogicalqualitieswereparticularlyappreciated,inthecombinationwitharatheradvancedtechnicalmaterial.

【目录】

Preface
O.Introduction:Notation，ElementaryResults
1SomeFactsAboutLowerandUpperBounds
2TheSetofExtendedRealNumbers
3LinearandBilinearAlgebra
4DifferentiationinaEuclideanSpace
5Set-ValuedAnalysis
6RecallsonConvexFunctionsoftheRealVariable
Exercises
A.ConvexSets
1Generalities
2ConvexSetsAttachedtoaConvexSet
3ProjectionontoClosedConvexSets
4SeparationandApplications
5ConicalApproximationsofConvexSets
Exercises
B.ConvexFunctions
1BasicDefinitionsandExamples
2FunctionalOperationsPreservingConvexity
3LocalandGlobalBehaviourofaConvexFunction
4First-andSecond-OrderDifferentiation
Preface
O.Introduction:Notation，ElementaryResults
1SomeFactsAboutLowerandUpperBounds
2TheSetofExtendedRealNumbers
3LinearandBilinearAlgebra
4DifferentiationinaEuclideanSpace
5Set-ValuedAnalysis
6RecallsonConvexFunctionsoftheRealVariable
Exercises
A.ConvexSets
1Generalities
2ConvexSetsAttachedtoaConvexSet
3ProjectionontoClosedConvexSets
4SeparationandApplications
5ConicalApproximationsofConvexSets
Exercises
C.SublinearityandSupportFunctions
1SublinearFunctions
2TheSupportFunctionofaNonemptySet
3CorrespondenceBetweenConvexSetsandSublinearFunctions
Exercises
D.SubdifferentialsofFiniteConvexFunctions
1TheSubdifferential:DefinitionsandInterpretations
2LocalPropertiesoftheSubdiffrential
3FirstExamples
4CalculusRuleswithSubdifferentials
5FurtherExamples
6TheSubdifferentialasaMultifunction
Exercises
E.ConjugacyinConvexAnalysis
1TheConvexConjugateofaFunction
2CalculusRulesontheConjugacyOperation
3VariousExamples
4DifferentiabilityofaConjugateFunction
Exercises
BibliographicalComments
TheFoundingFathersoftheDiscipline
References
Index