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I am trying to derive the close form expression for the update of $\omega_i$ in coordinate descent for lasso, but I find it hard to proceed. Could you give me some hints?

$min_\omega\sum_{i=1}^m(y_i-X_i\cdot\omega)^2+\lambda\|\omega\|_1$ I need to find $\omega_i = ?$

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You can find the derivation in different forms at the following links:

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