A derivative free optimization algorithm in practice

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.