This paper considers wireless-powered relaying multiple-input-multiple-output (MIMO) communication, where all four nodes (information source, energy source, relay, and destination) are equipped with multiple antennas. Orthogonal frequency division multiplexing (OFDM) is applied for information processing to compensate the frequency selectivity of communication channels between the information source and the relay and between the relay and the destination as these nodes are assumed to be located far apart each other. The relay is equipped with a full-duplexing interface for harvesting energy not only from the wireless transmission of the dedicated energy source but also from its own transmission while relaying the source information to the destination. The problem of designing the optimal power allocation over OFDM subcarriers and transmit antennas to maximize the overall spectral efficiency is addressed. Due to a very large number of subcarriers, this design problem poses a large-scale nonconvex optimization problem involving a few thousand variables of power allocation, which is very computationally challenging. A novel path-following algorithm is proposed for computation. Based on the developed closed-form calculation of linear computational complexity at each iteration, the proposed algorithm rapidly converges to an optimal solution. Compared to the best existing solvers, the computational complexity of the proposed algorithm is reduced at least 105 times, making it really efficient and practical for online computation while that existing solvers are impotent. Numerical results for a practical simulation setting show promising results by achieving high spectral efficiency.