How much do approximate derivatives hurt filter methods?

In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.