The wood material for violin bows from the pernambuco tree (Caesalpina echinata) has large individual variations in the density. For high quality bows, the higher densities are preferred, but since pernambuco is rather rare and expensive, it is of interest to investigate if it is possible to compensate for density variations in the wood material, at the same time as important qualities of the bow are unchanged. In this study, numerical optimization is used to recover the static and dynamic properties of a reference bow, on a bow with 10% lower density. The structural calculations of the bows are made with a umerical model in the finite element program ANSYS, which in its is coupled to an external, gradient based optimiztion routine. The automatic optimization process is performed with a routine called the Method of Moving Asymptotes (MMA).