基本信息

书名:变分分析

定价：99.00元

作者: 洛克菲勒 (R.Tyrrell Rockafellar)， Roger

出版社：世界图书出版公司

出版日期：2013_10_01

ISBN：9787510061363

字数：

页码：734

版次：1

装帧：平装

开本：24开

商品重量：

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内容提要

　　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

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