Approximating Hessians in multilevel unconstrained optimization

                     V. Malmedy and Ph. L. Toint
     
                     Report 08/19  December 2008

Abstract.  We consider Hessian approximation schemes for large-scale
multilevel unconstrained optimization problems, which typically present a
sparsity and partial separability structure.  This allows iterative
quasi-Newton methods to solve them despite of their size.  Structured
finite-difference methods and updating schemes based on the secant equation
are presented and compared numerically inside the multilevel trust-region
algorithm proposed by Gratton, Mouffe, Toint and Weber (2008).