{i+1} {-} g_{i})}{p_i^T (g_{i+1} {-} g_{i})} $$" style="width:49px;height:14px;"></p><p><b>Negative update coefficients</b></p><p>In cases where the update coefficient <img src="ncg_doc_eq11960540003268942809.png" alt="$\beta_{i+1} < 0$" style="width:20px;height:6px;">, it is set to <img src="ncg_doc_eq00202142981986870057.png" alt="$0$" style="width:3px;height:4px;"> to avoid directions that are not descent directions [3].</p><p><b>Restart procedures</b></p><p>The NCG iterations are restarted every <i>n</i