We investigate the joint problem of relay selection and optimal sharing of relay power in wireless cellular networks with multicast traffic. We use two different performance metrics to maximize the network performance. We first present a mixed Boolean-convex optimization model to maximize the overall network capacity and solve this combinatorial problem optimally using branch and bound technique. We then show that obtaining the optimal solution is computationally not feasible for large network sizes and, unlike the case of unicast traffic, a water filling method does not yield near optimal solutions in multicast scenarios. We thus adopt an algorithm based on sequential fixing which substantially reduces the computation time and achieves near optimal solutions. In addition, we present a mixed integer linear programming model to maximize the capacity of the minimum capacity link and show that the model is very efficient to reach the optimal solutions.
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