In this work we present an adaptive parameterization strategy for the so-called sequential solution approach where the optimization problem is approximated by a nonlinear program (NLP) by parameterization of the control variables only. The proposed method is embedded into a solution methodology where a hierarchy of successively refined finite dimensional optimization problems are solved. Information on the solution of the coarser approximation is used to construct a fully adaptive, problem dependent parameterization. The adaptation is built on a multiscale setting involving wavelets. We demonstrate examplarily that the adaptive parameterization is more efficient and robust compared with a uniform parameterization of comparable accuracy.