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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$\nabla^2f\succeq 0$。