凸函数的几何理解

凸函数的几何理解：

Let {\displaystyle X} be a convex set in a real vector space and let {\displaystyle f:X\rightarrow {\text{R}}} be a function.

• f is called convex if:

{\displaystyle \forall x_{1},x_{2}\in X,\forall t\in [0,1]:\qquad f(tx_{1}+(1-t)x_{2})\leq tf(x_{1})+(1-t)f(x_{2}).}

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