凸优化理论

图书标准信息

• 作者 [美]博赛克斯（Dimitri P.Bertsekas） 著
• 出版社 清华大学出版社
• 出版时间 2011-01
• 版次 1
• ISBN 9787302237600
• 定价 49.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 494页
• 字数 1111千字
• 正文语种 简体中文
• 丛书 清华版双语教学用书

【内容简介】

　　《凸优化理论（影印版）》作者德梅萃·博赛克斯教授是优化理论的国际知名学者，现任美国麻省理工学院电气工程与计算机科学系教授，曾在斯坦福大学工程经济系和伊利诺伊大学电气工程系任教，在优化理论、控制工程、通信工程、计算机科学等领域有丰富的科研教学经验，成果丰硕。博赛克斯教授是一位多产作者，著有14本专著和教科书。《凸优化理论（影印版）》是作者在优化理论与方法的系列专著和教科书中的一本，自成体系又相互对应。主要内容分为两部分：凸分析和凸问题的对偶优化理论。

【目录】

1BasicConceptsofConvexAnalysis
1.1ConvexSetsandFunctions
1.1.1ConvexFunctions
1.1.2ClosednessandSemicontinuity
1.1.3OperationswithConvexFunctions
1.1.4CharacterizationsofDifferentiableConvexFunctions
1.2ConvexandAffineHulls
1.3RelativeInteriorandClosure
1.3.1CalculusofRelativeInteriorsandClosures
1.3.2ContinuityofConvexFunctions
1.3.3ClosuresofFunctions
1.4RecessionCones
1.4.1DirectionsofRecessionofaConvexFunction
1.4.2Nonemptine~sofIntersectionsofClosedSets
1.4.3ClosednessUnderLinearTransformations
1.5Hyperplanes
1.5.1HyperplaneSeparation
1.5.2ProperHyperplaneSeparation
1.5.3NonverticalHyperplaneSeparation
1.6ConjugateFunctions
1.7Summary

2BasicConceptsofPolyhedralConvexity
2.1ExtremePoints
2.2PolarCones
2.3PolyhedralSetsandFunctions
2.3.1PolyhedralConesandFarkas'Lemma
2.3.2StructureofPolyhedralSets
2.3.3PolyhedralFunctions
2.4PolyhedralAspectsofOptimization

3BasicConceptsofConvexOptimization
3.1ConstrainedOptimization
3.2ExistenceofOptimalSolutions
3.3PartialMinimizationofConvexFunctions
3.4SaddlePointandMinimaxTheory

4GeometricDualityFramework
4.1MinCommon/MaxCrossingDuality
4.2SomeSpecialCases
4.2.1ConnectiontoConjugateConvexFunctions
4.2.2GeneralOptimizationDuality
4.2.3OptimizationwithInequalityConstraints
4.2.4AugmentedLagrangianDuality
4.2.5MinimaxProblems
4.3StrongDualityTheorem
4.4ExistenceofDualOptimalSolutions
4.5DualityandPolyhedralConvexity
4.6Summary

5DualityandOptimization
5.1NonlinearFarkas'Lemma
5.2LinearProgrammingDuality
5.3ConvexProgrammingDuality
5.3.1StrongDualityTheorem-Inequality.Constraints
5.3.2OptimalityConditions
5.3.3PartiallyPolyhedralConstraints
5.3.4DualityandExistenceofOptimalPrimalSolutions
5.3.5FenchelDuality
5.3.6ConicDuality
5.4SubgradientsandOptimalityConditions
5.4.1SubgradientsofConjugateFunctions
5.4.2SubdifferentialCalculus
5.4.3OptimalityConditions
5.4.4DirectionalDerivatives
5.5MinimaxTheory
5.5.1MinimaxDualityTheorems
5.5.2SaddlePointTheorems
5.6TheoremsoftheAlternative
5.7NonconvexProblems
5.7.1DualityGapinSeparableProblems
5.7.2DualityGapinMinimaxProblems

AppendixA：MathematicalBackground
NotesandSources
SupplementaryChapter6onConvexOptimizationAlgorithms