变分分析

图书标准信息

• 作者 [美]洛克菲勒（R.Tyrrell Rockafellar）、[美]Roger J-B Wets 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 1
• ISBN 9787510061363
• 定价 99.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 734页
• 正文语种 英语

【内容简介】

　　Inthisbookweaimtopresent，inaunifiedframework，abroadspectrumofmathematicaltheorythathasgrowninconnectionwiththestudyofproblemsofoptimization，equilibrium，control，andstabilityoflinearandnonlinearsystems.ThetitleVariationalAnalysisrefiectsthisbreadth.
　　Foralongtime，variationalproblemshavebeenidentifiedmostlywiththe'calculusofvariations'.Inthatvenerablesubject，builtaroundtheminimizationofintegralfunctionals，constraintswererelativelysimpleandmuchofthefocuswasoninfinite-dimensionalfunctionspaces.Amajorthemewastheexplorationofvariationsaroundapoint，withintheboundsimposedbytheconstraints，inordertohelpcharacterizesolutionsandportraythemintermsof'variationalprinciples'.Notionsofperturbation，approximationandevengeneralizeddifferentiabilitywereextensivelyinvestigated，Variationaltheoryprogressedalsotothestudyofso-calledstationarypoints，criticalpoints，andotherindicationsofsingularitythatapointmighthaverelativetoitsneighbors，especiallyinassociationwithexistencetheoremsfordifferentialequations.

【目录】

Chapter1.MaxandMin
A.PenaltiesandConstraints
B.EpigraphsandSemicontinuity
C.AttainmentofaMinimum
D.Continuity,ClosureandGrowth
E.ExtendedArithmetic
F.ParametricDependence
G.MoreauEnvelopes
H.Epi-AdditionandEpi-Multiplication
I*.AuxiliaryFactsandPrinciples
Commentary

Chapter2.Convexity
A.ConvexSetsandFunctions
B.LevelSetsandIntersections
C.DerivativeTests
D.ConvexityinOperations
E.ConvexHulls
F.ClosuresandContimuty
G.*Separation
H*RelativeInteriors
I*PiecewiseLinearFunctions
J*OtherExamples
Commentary

Chapter3.ConesandCosmicClosure
A.DirectionPoints
B.HorizonCones
C.HorizonFunctions
D.CoercivityProperties
E*ConesandOrderings
F*CosmicConvexity
G*PositiveHulls
Commentary

Chapter4.SetConvergence
A.InnerandOuterLimits
B.Painleve-KuratowskiConvergence
C.Pompeiu-HausdorffDistance
D.ConesandConvexSets
E.CompactnessProperties
F.HorizonLimits
G*ContimutyofOperations
H*QuantificationofConvergence
I*HyperspaceMetrics
Commentary

Chapter5.Set-ValuedMappings
A.Domains,RangesandInverses
B.ContinuityandSemicontimuty
C.LocalBoundedness
D.TotalContinuity
E.PointwiseandGraphicalConvergence
F.EquicontinuityofSequences
G.ContinuousandUniformConvergence
H*MetricDescriptionsofConvergence
I*OperationsonMappings
J*GenericContinuityandSelections
Commentary.

Chapter6.VariationalGeometry
A.TangentCones
B.NormalConesandClarkeRegularity
C.SmoothManifoldsandConvexSets
D.OptimalityandLagrangeMultipliers
E.ProximalNormalsandPolarity
F.Tangent-NormalRelations
G*RecessionProperties
H*IrregularityandConvexification
I*OtherFormulas
Commentary

Chapter7.EpigraphicalLimits
A.PointwiseConvergence
B.Epi-Convergence
C.ContinuousandUniformConvergence
D.GeneralizedDifferentiability
E.ConvergenceinMinimization
F.Epi-ContinuityofFunction-ValuedMappings
G.ContinuityofOperations
H*TotalEpi-Convergence
I*Epi-Distances
J*SolutionEstimates
Commentary

Chapter8.SubderivativesandSubgradients
A.SubderivativesofFunctions
B.SubgradientsofFunctions
C.ConvexityandOptimality
D.RegularSubderivatives
E.SupportFunctionsandSubdifferentialDuality
F.Calmness
G.GraphicalDifferentiationofMappings
H*Proto-DifferentiabilityandGraphicalRegularity
I*ProximalSubgradients
J*OtherResults
Commentary

Chapter9.LipschitzianProperties
A.Single-ValuedMappings
B.EstimatesoftheLipschitzModulus
C.SubdifferentialCharacterizations
D.DerivativeMappingsandTheirNorms
E.LipschitzianConceptsforSet-ValuedMappings
……

Chapter10.SubdifferentialCalculus
Chapter11.Dualization
Chapter12.MonotoneMappings
Chapter13.Second-OrderTheory
Chapter14.Measurability