On the Global Convergence of Derivative Free Methods for Unconstrained Optimization

In this paper, starting from the study of the common elements that some globally convergent direct search methods share, a general convergence theory is established for unconstrained minimization methods employing only function values. The introduced convergence conditions are useful for developing and analyzing new derivative-free algorithms with guaranteed global convergence. As examples, we describe three new algorithms which combine pattern and line search approaches.