  This paper is devoted to the analysis of worst case complexity bounds for
linesearch-type derivative-free algorithms for the minimization of general
non-convex smooth functions. We prove that two linesearch-type algorithms enjoy
the same complexity properties which have been proved for pattern and direct
search algorithms. In particular, we consider two derivative-free algorithms
based on two different linesearch techniques and manage to prove that the
number of iterations and of function evaluations required to drive the norm of
the gradient of the objective function below a given threshold $\epsilon$ is
${\cal O}(\epsilon^{-2})$ in the worst case.
