\emph{7.} &amp; \qquad Compute $\beta_{i+1}$\\&#xA;\emph{8.} &amp; \qquad Set $p_{i+1} = -g_{i+1} + \beta_{i+1} p_i$\\&#xA;\emph{9.} &amp; \qquad Set $i = i + 1$\\&#xA;\emph{10.} &amp; \textbf{end while}\\&#xA;\emph{11.} &amp; Output: $x_i \approx x^*$\\&#xA;\end{tabular}&#xA;$$" style="width:146px;height:71px;"></p><p><b>Conjugate direction updates</b></p><p>The computation of <img src="ncg_doc_eq08047493418710975323.png" alt="$\beta_{i+1}$" style="width:9px;height:6px;"> in Step 7 above leads to different