两类带非正定邻近项的乘子交替方向法的收敛性分析

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1、目录i目目目录录录目录······································································i摘要······································································iiiAbstract·································································v1绪论················

2、···················································11.1研究背景及意义···················································11.2研究现状··························································11.3本文主要研究内容·················································52预备知识····

3、··························································72.1基本假设及定义···················································72.2相关引理··························································83第一类带非正定邻近正则项的交替方向法·······························93.1算法1的预测-校正

4、形式·············································93.2收敛性分析························································113.3遍历意义下的收敛速率·············································203.4数值模拟··························································223.4.1LASS

5、O模型···············································223.4.2全变差(TV)降噪模型·······································234第二类带非正定邻近项的交替方向法···································294.1算法2的预测-校正形式·············································294.2遍历意义下的收敛速率·············

6、································314.3数值模拟··························································344.3.1LASSO模型···············································354.3.2全变差(TV)降噪模型·······································36ii西南大学硕士学位论文5总结与展望·············

7、···············································435.1本文工作的总结···················································435.2未来工作的展望···················································43参考文献·································································45致谢··

8、····································································49已完成文章目录···························································51目录摘要两类带非正定邻近项的乘子交替方向法的收敛性分析运筹学与控制论专业硕士研究生王逸云指导教师陈加伟副教授摘要近些年来,作为解决具有可分离结构的多块线性约束凸优化模型的通用方法,乘子交替方向法(ADMM)得到了广泛的认可.