We use the parabolic wave equation to study the propagation of x-rays in tapered waveguides by numercial simulation and optimization. The goal of the study is to elucidate how beam concentration can be best achieved in x-ray optical nanostructures. Such optimized waveguides can e.g. be used to investigate single biomolecules. Here, we compare tapering geometries, which can be parametrized by linear and third-order (Bezier-type) functions and can be fabricated using standard e-beam litography units. These geometries can be described in two and four-dimensional parameter spaces, respectively. In both geometries, we observe a rugged structure of the optimization problems ``gain landscape. Thus, the optimization of x-ray nanostructures in general will be a highly nontrivial optimization problem.
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