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Exercise 3.4.9

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Let $L = \frac{1}{2} ∥ x ∥^{2} + \frac{1}{2} ∥ x - v ∥^{2} = \frac{1}{2} x^{T} x + \frac{1}{2} {(x - v)}^{T} (x - v)$ , take derivative w.r.t. $x$ , we have

\begin{array}{l} \frac{∂L}{∂x} & = x + x - v \\ = 2 x - v \end{array}

Let the derivative equal to 0, we see ${Prox}_{F} (v) = argmin L = \frac{v}{2}$

niuers

2020-03-20 00:00

Exercise 3.4.9

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