An algorithm using quadratic interpolation
 for unconstrained derivative free optimization
     
          A. R. Conn and Ph. L. Toint

                 Report 95/6

This  paper  explores   the  use  of   multivariate
interpolation techniques  in the context of methods
for unconstrained  optimization that do not require
derivative  of   the  objective  function.   A  new
algorithm is proposed that uses quadratic models in
a  trust  region  framework.   The   algorithm   is
constructed  to  require  few  evaluations  of  the
objective function and is designed to be relatively
insensitive  to  noise  in the  objective  function
values.  Its performance is analyzed on a set of 20
examples, both with and without noise.