凸优化笔记(非常零碎)
1. Lipschitz Funcion(李比西斯函数)
对于不光滑(nonsomooth)的凸函数的分析引入了Lipschitz functions:
定义:
2.Nonexpansiveness of Projection(投影的非延展性)
Projection operator is non-expansive means:
也就是说, 投影操作是L小于1的L-Lipschitz function.
,要证明这个不等式。
定义投影操作(projection operator):
x can be in or outside . The projection x onto C is:
引入一些要用的东西:
Projection Theorem(obtuse angle criterion):
Variational Characterization:
Reference:
关于【2】非延展性的证明参考:https://angms.science/doc/CVX/CVX_ProjectionIsNonexpansive.pdf