Exploiting problem structure in pattern-search 
               methods for unconstrained optimization

                   C. Price and Ph. L. Toint

         Report 04/01                     12th January 2004

A direct search method for unconstrained optimization is described.  The
method makes use of any partial separability structure that the objective
function may have.  The method uses successively finer nested grids, and
minimizes the objective function over each grid in turn.  All grids are
aligned with the coordinate directions which allows the partial separability
structure of the objective function to be exploited.  This has two advantages:
it reduces the work needed to calculate function values at the points
required; and it provides function values at other points as a free
by-product.  Numerical results show that using partial separability can
dramatically reduce the number of function evaluations needed to minimize a
function, in some cases allowing problems with thousands of variables to be
solved.