Optimal resource allocation in interference networks requires the solution of non-convex optimization problems. Except from treating interference as noise (IAN) one usually has to optimize jointly over the achievable rates and transmit powers. This non-convexity is normally only due to the transmit powers while the rates are linear. Conventional approaches like the Polyblock Algorithm treat all variables equally and, thus, require a two layer solver to exploit the linearity in the rates and keep the computational complexity at a reasonable level. In this paper, we develop a branch and bound algorithm that exploits most of the problem structure and, compared to previous algorithms, has significantly better performance, improved numerical stability and provides a feasible solution even if terminated prematurely. We employ this novel algorithm to study throughput optimal power allocation in a multi-way relay channel with simultaneous non-unique decoding and rate splitting (RS) encoders. We evaluate the performance gains of RS over "pure" SND and IAN numerically. While SND often achieves significantly higher throughput than IAN the benefits of rate splitting are not that pronounced on average and largely depend on the channel condition.