凸分析（英文版）

图书标准信息

• 作者 [德]洛克菲拉 著
• 出版社 世界图书出版公司
• 出版时间 2011-01
• 版次 1
• ISBN 9787510029608
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 451页
• 正文语种 英语

【内容简介】

convexityhasbeenincreasinglyimportantinrecentyearsinthestudyofextremumproblemsinmanyareasofappliedmathematics.thepurposeofthisbookistoprovideanexpositionofthetheoryofconvexsetsandfunctionsinwhichapplicationstoextremumproblemsplaythecentralrole.
systemsofinequalities，theminimumormaximumofaconvexfunctionoveraconvexset，lagrangemultipliers，andminimaxtheoremsareamongthetopicstreated，aswellasbasicresultsaboutthestructureofconvexsetsandthecontinuityanddifferentiabilityofconvexfunctionsandsaddle-functions.dualityisemphasizedthroughout，particularlyintheformoffenchersconjugacycorrespondenceforconvexfunctions.

【目录】

Preface.
IntroductoryRemarks：aGuidefortheReader
PARTl：BASICCONCEPTS
1.AffineSets
2.ConvexSetsandCones
3.TheAlgebraofConvexSets
4.ConvexFunctions
5.FunctionalOperations

PARTII：TOPOLOGICALPROPERTIES
6.RelativeInteriorsofConvexSels
7.ClosuresofConvexFunctions
8.RecessionConesandUnboundedness
9.SomeCIosednessCriteria
10.ContinuityofConvexFunctions

PARTⅢ：DUALITYCORRESPONDENCES
11.SeparationTheorems
12.ConjugatesofConvexFunctions
13.SupportFurctions
14.PolarsofConvexSets
15.PolarsofConvexFunctions
16.DualOperations

PARTIV：REPRESENTATIONANDINEQUALITIES
17.Carath6odorysTheorem
18.ExtremePointsandFacesofConvexSets
19.PolyhedralConvexSetsandFunctions
20.SomeApplicationsofPolyhedralConvexity
21.HellysTheoremandSystemsofInequalities
22.LinearInequalities
CONTENTS

PARTV：DIFFERENTIALTHEORY
23.DirectionalDerivativesandSubgradients
24.DifferentialContinuityandMonotonicity
25.DifferentiabilityofConvexFunctions
26.TheLegendreTransformation

PARTVI：CONSTRAINEDEXTREMUMPROBLEMS
27.TheMinimumofaConvexFunction
28.OrdinaryConvexProgramsandLagrangeMultipliers
29.BifunctionsandGeneralizedConvexPrograms
30.AdjointBifunctionsandDualPrograms
31.FenchelsDualityTheorem
32.TheMaximumofaConvexFunction

PARTVII：SADDLE-FUNCTIONSANDMINIMAXTHEORY
33.Saddle-Functions
34.ClosuresandEquivalenceClasses
35.ContinuityandDifferentiabilityofSaddle-functions
36.MinimaxProblems
37.ConjugateSaddle-functionsandMinimaxTheorems
PARTVIII：CONVEXALGEBRA
38.TheAlgebraofBifunctions
39.ConvexProcesses.
CommentsandReferences
Bibliography
Index