ual-max"></a>
Dual coordinate maximization</h1>
<p>The updated dual objective can be expanded as: </p><p class="formulaDsp">
\[ D(\balpha_t + \be_q \Delta\alpha_q) = \text{const.} - \frac{1}{2\lambda n^2} \bx_q^\top \bx_q (\Delta\alpha_q)^2 - \frac{1}{n} \bx_q^\top \frac{X\alpha_t}{\lambda n} \Delta\alpha_q - \frac{1}{n} \ell^*_q(- \alpha_q - \Delta\alpha_q) \]
</p>
<p> This can also be written as </p><p class="formulaDsp">
\begin{align*} D(\balpha_t + \be_q \Delta\alpha_q) &amp;\propto - \frac{A}{2} (\Delt