a\alpha_q)^2 - B \Delta\alpha_q - \ell^*_q(- \alpha_q - \Delta\alpha_q), \\ A &amp;= \frac{1}{\lambda n} \bx_q^\top \bx_q = \frac{1}{\lambda n} \| \bx_q \|^2, \\ B &amp;= \bx_q^\top \frac{X\balpha_t}{\lambda n} = \bx_q^\top \bw_t. \end{align*}
</p>
<p> Maximizing this quantity in the scalar variable \(\Delta\balpha\) is usually not difficult. It is convenient to store and incrementally update the model \(\bw_t\) after the optimal step \(\Delta\balpha\) has been determined: </p><p class="formulaDsp">
\[ \bw_