Sensitivity of trust-region algorithms on their parameters N. Gould, D. Orban, A. Sartenaer Ph. L. Toint Report 04/07 August 10th, 2004 In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommanded ranges of values for these parameters are exhibited on the basis of extensive numerical tests. Keywords: unconstrained programming, trust-region methods, algorithmic parameters.