Fig. 3

Visualisation of Scolnik’s acceleration. The optimal line search parameter \(\alpha ^{*}\) yields the new iterate \({\mathbf {p}}^{k+1}\). Due to the construction of Scolnik’s acceleration, the vector \(\left( {\mathbf {p}}^{k+1}-{\mathbf {p}}^k\right)\) is perpendicular to the vector \(\left( {\mathbf {p}}^{k+1}-{\mathbf {p}}^{*}\right)\) (indicated by the green dashed line)