We present a novel approach to maximize the transmission rate in a MIMO relay system, where all nodes are equipped with multiple antennas and the relay is self-sustained by harvesting energy using a non-uniform power splitting method. By deriving a closed-form solution for the optimal power splitting ratios for harvesting at the relay and the optimal power allocation for precoding at both source and relay, we are able to design an efficient primal-dual algorithm to jointly optimize for these variables, instead of solving for them sequentially as traditionally done. We demonstrate the algorithm efficiency at reducing the run-time by several orders of magnitude compared to standard solvers and existing sequential algorithms, making our algorithm highly amenable to massive MIMO settings. Numerical results further reveal the significant rate gain of non-uniform power splitting over traditional uniform splitting.