On the complexity of the steepest-descent
                       with exact linesearches

             C. Cartis, N. I. M. Gould and Ph. L. Toint

                    NAXYS-16-2012     September 2012

The worst-case complexity of the steepest-descent algorithm with exact
linesearches for unconstrained smooth optimization is analyzed, and it is shown
that the number of iterations of this algorithm which may be necessary to find
an iterate at which the norm of the objective function's gradient is less that
a prescribed $\epsilon$ is, essentially, a multiple of $1/\epsilon^2$, as is
the case for variants of the same algorithms using inexact linesearches.