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任意二次可微一维函数符号$f: \mathbb{R}^{n} \rightarrow \mathbb{R}$与二次可微多维函数$f: \mathbb{R}^{n} \rightarrow \mathbb{R}$重复，容易造成误解，因此将原文改为$f: \mathbb{R} \rightarrow \mathbb{R}$，即：更正式地讲，$f$为凸函数，当且仅当任意二次可微一维函数$f: \mathbb{R} \rightarrow \mathbb{R}$是凸的。对于任意二次可微多维函数$f: \mathbb{R}^{n} \rightarrow \mathbb{R}$，它是凸的当且仅当它的Hessian$\nabla^2f\succeq 0$。
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任意二次可微一维函数符号$f: \mathbb{R}^{n} \rightarrow \mathbb{R}$与二次可微多维函数$f: \mathbb{R}^{n} \rightarrow \mathbb{R}$重复，英文原版为$f: \mathbb{R} \rightarrow \mathbb{R}$，因此将原文改为$f: \mathbb{R} \rightarrow \mathbb{R}$，即：更正式地讲，$f$为凸函数，当且仅当任意二次可微一维函数$f: \mathbb{R} \rightarrow \mathbb{R}$是凸的。对于任意二次可微多维函数$f: \mathbb{R}^{n} \rightarrow \mathbb{R}$，它是凸的当且仅当它的Hessian$\nabla^2f\succeq 0$。