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@@ -195,12 +195,12 @@ $$
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a. 当$\vert z^i\vert>\frac{\lambda}{L}$时，由上述推导可知$g(x_i)$的最小值在$x^i=z^i-\frac{\lambda}{L}$处取得，令
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a. 当$\vert z^i\vert>\frac{\lambda}{L}$时，由上述推导可知$g(x_i)$的最小值在$x^i=z^i-\frac{\lambda}{L}$处取得，令
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$$
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$$
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- \begin{align}
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+ \begin{aligned}
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f(x^i)&=g(x^i)\vert_{x^i=0}-g(x^i)\vert_{x_i=z^i-\frac{\lambda}{L}}\\
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f(x^i)&=g(x^i)\vert_{x^i=0}-g(x^i)\vert_{x_i=z^i-\frac{\lambda}{L}}\\
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&=\frac{L}{2}\left({z^i}\right)^2 - \left(\lambda z^i-\frac{\lambda^2}{2L}\right)\\
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&=\frac{L}{2}\left({z^i}\right)^2 - \left(\lambda z^i-\frac{\lambda^2}{2L}\right)\\
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&=\frac{L}{2}\left(z^i-\frac{\lambda}{L}\right)^2\\
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&=\frac{L}{2}\left(z^i-\frac{\lambda}{L}\right)^2\\
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&>0
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&>0
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- \end{align}
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+ \end{aligned}
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$$
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$$
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Sm1les