目 录
中文摘要
ABSTRACT
第一章 绪 论............................................................................................................... 1
§1.1 研究背景及意义............................................................................................... 1
§1.2 研究内容及章节安排 ....................................................................................... 2
第二章 计算复杂性和算法研究现状 ......................................................................... 5
§2.1 引言................................................................................................................... 5
§2.2 计算复杂性....................................................................................................... 5
§2.3 研究现状 ..............................................................................................................................10
§2.4 小结................................................................................................................. 16
第三章 椭球法 ........................................................................................................... 17
§3.1 引 言............................................................................................................... 17
§3.2 椭球法 ............................................................................................................ 17
§3.2.1 割平面思想.............................................................................................. 17
§3.2.2 Khanchian椭球法 ..................................................................................... 19
§3.2.3 椭球法的改进........................................................................................... 21
§3.3 仿真实践 ......................................................................................................... 26
§3.4 小结 ................................................................................................................ 27
第四章 内点法 ........................................................................................................... 29
§4.1 引 言.............................................................................................................. 29
§4.2 内点法思想及主要概念 ................................................................................ 29
§4.2.1 投影法...................................................................................................... 29
§4.2.2 仿射尺度法............................................................................................... 32
§4.2.3 路径跟踪法.............................................................................................. 35
§4.3 原-对偶内点法................................................................................................ 35
§4.3.1 原-对偶算法基本思想 ............................................................................. 35
§4.3.2 原-对偶路径跟踪法 ................................................................................. 37
§4.4 本章小结 ........................................................................................................ 39
第五章 自协调函数 ................................................................................................... 41
§5.1 引 言.............................................................................................................. 41
§5.2 自协调函数 .................................................................................................... 41
§5.2.1 自协调函数描述...................................................................................... 41
§5.2.2 牛顿法...................................................................................................... 43
§5.2.3 收敛性证明.............................................................................................. 45
§5.2.4 自协调理论分析...................................................................................... 49
§5.3 构造自协调函数 ............................................................................................ 55
§5.4 本章小结 ........................................................................................................ 62
第六章 结论与展望 ................................................................................................... 63
§6.1 结 论.............................................................................................................. 63