锥优化的基于核函数的内点算法

图书标准信息

• 作者 袁亚湘 编
• 出版社 科学出版社
• 出版时间 2010-01
• 版次 1
• ISBN 9787030280268
• 定价 38.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 135页
• 正文语种 英语
• 丛书 运筹与管理科学丛书9

【内容简介】

　　《锥优化的基于核函数的内点算法》共分七章，第1章介绍锥优化理论方法的发展历程，第2章介绍核函数及其性质、由核函数确定的障碍函数的性质，第3～6章分别介绍中心路径的概念、锥的代数性质，给出求解线性规划问题、P*(k)线性互补问题、半正半优化问题、二阶锥优化问题的基于核函数的内点算法，分析了大步算法、小步内点算法的计算复杂性。
　　《锥优化的基于核函数的内点算法》可作为运筹学专业的本科生、研究生关于内点算法的入门书，同时也可作为研究人员的关于内点算法的参考书。

【目录】

Preface
Chapter1Introduction
1.1Conicoptimizationproblems
1.2Conicduality
1.3Fromthedualconetothedualproblem
1.4Developmentoftheinterior-pointmethods
1.5Scopeofthebook
Chapter2KernelFunctions
2.1Definitionofkernelfunctionsandbasicproperties
2.2Thefurtherconditionsofkernelfunctions
2.3Propertiesofkernelfunctions
2.4Examplesofkernelfunctions
2.5Barrierfunctionsbasedonkernelfunctions
2.6Generalizationofkernelfunction
2.6.1Finitekernelfunction
2.6.2Parametrickernelfunction
Chapter3KernelFunction-basedInterior-pointAlgorithmforLO
3.1ThecentralpathforLO
3.2ThesearchdirectionsforLO
3.3Thegenericprimal-dualinterior-pointalgorithmforLO
3.4Analysisofthealgorithm
3.4.1Decreaseofthebarrierfunctionduringaninneriteration
3.4.2Choiceofthestepsize
3.5Iterationbounds
3.6Summaryofcomputationforcomplexitybound
3.7Complexityanalysisbasedonkernelfunctions
3.8Summaryofresults
Chapter4KernelFunction-basedInterior-pointAlgorithmforP*(k)LCP
4.1TheP*(k)-LCP
4.2ThecentralpathforP*(k)-LCP
4.3ThenewsearchdirectionsforP*(k)-LCP
4.4Thegenericprimal-dualinterior-pointalgorithmforP*(k)-LCP...
4.5Thepropertiesofthebarrierfunction
4.6Analysisofthealgorithm
4.6.1Growthbehaviorofthebarrierfunction
4.6.2Determiningthedefaultstepsize
4.7Decreaseofthebarrierfunctionduringaninneriteration
4.8Complexityofthealgorithm
4.8.1Iterationboundforthelarge-updatemethods
4.8.2Iterationboundforthesmall-updatemethods
Chapter5KernelFunction-basedInterior-pointAlgorithmforSDO
5.1Specialmatrixfunctions
5.2ThecentralpathforSDO
5.3ThenewsearchdirectionsforSDO
5.4Thegenericprimal-dualinterior-pointalgorithmforSDO
5.5Thepropertiesofthebarrierfunction
5.6Analysisofthealgorithm
5.6.1Decreaseofthebarrierfunctionduringaninneriteration
5.6.2Choiceofthestepsize
5.7Iterationbounds
5.8Kernelfunction-basedschemes
5.9Theexample
5.10Numericalresults
Chapter6KernelFunction-basedInterior-pointAlgorithmforSOCO
6.1Algebraicpropertiesofsecond-ordercones
6.2Barrierfunctionsdefinedonsecond-ordercone
6.3Rescalingthecone
6.4ThecentralpathforSOCO
6.5ThenewsearchdirectionsforSOCO
6.6Thegenericprimal-dualinterior-pointalgorithmforSOCO
6.7Analysisofthealgorithm
6.8Thecrucialinequality
6.9Decreaseofthebarrierfunctionduringaninneriteration
6.10Increaseofthebarrierfunctionduringaμ-update
6.11Iteration-bounds
6.12Numericalresults
6.13Sometechnicallemmas
AppendixThreeTechnicalLemmas
Reference