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Could someone point me to a reference on how to find $w$ as the minimizer of:

$$ \frac{1}{2}\sum_{i=1}^{d}q_i(w_i-m_i)^2+\sum_{j=1}^{n}log(1+\exp(-y_jw^Tx_j)) $$

where $q_i$ (initialized with $\lambda$) is a vector of regularization values for each parameter $w_i$ and $m_i$ (initialized with $0$) is the minimum values of $q_i$ found on the previous iteration of the regression.

The original algorithm can be found here: http://books.nips.cc/papers/files/nips24/NIPS2011_1232.pdf (Algorithm 3, page 6).

I don't seem to figure it out how to do it when $\lambda$ is not fixed but updated iteratively in $q_i$.

Thanks.

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