新書推薦:
《
技术与德国 : 1800年至今
》
售價:NT$
493.0
《
重返冰河时代:发现史前世界
》
售價:NT$
605.0
《
拉夫尔
》
售價:NT$
437.0
《
羞耻:规训的情感
》
售價:NT$
409.0
《
经济巨擘:思想碰撞与传承(精装典藏版)
》
售價:NT$
498.0
《
一如既往
》
售價:NT$
386.0
《
人工智能新时代:核心技术与行业赋能
》
售價:NT$
493.0
《
西方文明4000年(战争与和平,野蛮与文明,沉沦与觉醒,记录影响西方文明发展的历史瞬间)
》
售價:NT$
437.0
|
內容簡介: |
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.
|
目錄:
|
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
|
|