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凸集和凸函数 | ComputerScience #6

Open marchboy opened 4 years ago

marchboy commented 4 years ago

https://marchboy.github.io/2020/09/07/%E5%87%B8%E9%9B%86%E5%92%8C%E5%87%B8%E5%87%BD%E6%95%B0/

定义凸集若集合C内任意两点之间的线段均在集合C内,则称集合C为凸集。即对与凸集,它具备性质:$$若\forall x_1, x_2 \in C, \forall \theta \in [0,1],则x = \theta · x_1 + (1 - \theta) · x_2 \in C$$ 凸函数Reference: