We investigate the problem of Hölder functions optimization using Genetic Algorithms (GA). We first derive a relation between the Hölder exponent of the function, the sampling rate, and the accuracy of the optimum localization, both in the domain and the range of the function. This relation holds for any optimization method which work on sampled search spaces. We then present a finer analysis in the case of the use of a GA, which is based on a deceptivity analysis. Our approach uses a decomposition on the Haar basis, which reflects in a natural way the Hölder structure of the function. It allows to relate the deceptivity, the exponent and some parameters of the GA (including the sampling precision). These results provide some indications which may help to make the convergence of a GA easier.