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Results tagged with lagrange-multipliers
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user 193742
The method of Lagrange multipliers finds critical points (including maxima and minima) of a differentiable function subject to differentiable constraints.
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Rewrite $\frac{1}{2}||x-u||_2^2$ subject to $||x||_1\le c$ to lagrangian form with multiplie...
Define
$$G(x) \triangleq \sup_{\mu \geqslant 0} \mu \cdot \left( \|x\|_1 - c \right).$$
Now, if $\| x \|_1 \leqslant c$, $G(x) = 0$; otherwise, $G(x) = \infty$. Hence
\begin{align}
F(u, c) &= \inf_x \ …
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