On Iterated-Subspace Minimization Methods 
           for Nonlinear Optimization

           A. R. Conn, Nick Gould, 
        A. Sartenaer and Ph. L. Toint 

                Report 94/13

We    consider   a   class   of   Iterated-Subspace
Minimization (ISM) methods  for solving large-scale
unconstrained minimization problems.  At each major
iteration  of  such  a  method,  a  low-dimensional
manifold, the iterated subspace, is constructed and
an approximate minimizer of  the objective function
in  this  manifold  then determined.  The  iterated
subspace is  chosen to contain vectors which ensure
global  convergence of the overall  scheme and  may
also   contain   vectors   which   encourage   fast
asymptotic   convergence.    We   demonstrate   the
efficacy of this  approach on a collection of large
problems and indicate a number of avenues of future
research.