Tag Archive: Lagrange Multiplier

1. 直观解释   以二元函数为例，要寻找 $f(x, y)$ 在约束条件 $h(x, y) \leq 0$ 下的极值，即 $$ \begin{aligned} \min \; & f(x, y) \\ \mathrm{s.t.} \; & h(x, y) \leq 0 \end{aligned} \tag{1} $$   令…
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$$ \begin{aligned} \min \; & f(x, y) \\ \text{s.t.} \; & g(x, y) = 0 \end{aligned} \tag{1} $$   假设 $f(x, y)$ 在 $(x_0, y_0)$ 处取得极值 $z$，则在该处，$f(x, y) = z$ 和 $g(x, y) = 0$ 两条曲线应…
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1. 推导过程   以二元函数为例，要寻找 $f(x, y)$ 在约束条件 $g(x, y) = 0$ 下的极值，如 $$ \begin{aligned} \min \; & f(x, y) \\ \text{s.t.} \; & g(x, y) = 0 \end{aligned} \tag{1} $$   假设 $f(x, …
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