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This thesis deals with an optimization problem from the field of theoretical plasma physics. Specifically, it deals with the question of how the accelerated electrons are spatially arranged in a plasma wave generated by a laser pulse. An internal structure of this so-called witness beam is of interest for the radiation characteristics of such electron beams, in particular with regard to the coherence of the generated radiation. The resulting internal structure of the electron beam is a result of the interaction of the electrons with each other and the electric fields of the wakefield, therefore it is determined by solving a minimization problem. The thesis builds on previous results in this field and aims to find suggestions for improved algorithms to determine the minimum sought.