A Derivative Free Optimization Algorithm in Practice
 
               A. R. Conn     K. Scheinberg    Ph. L. Toint 

                              Report 98-11
 
We  consider  an algorithm   for   optimizing a nonlinear  function,  without
constraints, whose first  order derivatives exist but   are unavailable.  The
algorithm  is based  on approximating the  objective  function by a quadratic
polynomial interpolation  model and using  this  model within a  trust-region
framework. We study  some practical properties of  the algorithm and show how
this   algorithm can be  extended  to  solve certain constrained optimization
problems.    Computational results for  analytical  problems  and for applied
problems from the aeronautic industry are presented.