A linesearch algorithm with memory for unconstrained optimization


         N. I. M.  Gould  S. Lucidi  M. Roma  Ph. L. Toint\

                          Report 98/03

This paper considers algorithms for unconstrained nonlinear optimization
where the model used by the algorithm to represent the objective function
explicitly includes memory of the past iterations. This is intended to make
the algorithm less ``myopic'' in the sense that its behaviour is not
completely dominated by the local nature of the objective function, but
rather by a more global view.  We present a non-monotone linesearch
algorithm that has this feature and prove its global convergence.