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Interference is a common impairment in wireless communication systems. Multi-hop relay networks use a set of intermediate nodes called relays to facilitate communication between multiple transmitters and multiple receivers through multiple hops. Relay based communication is especially sensitive to interference because the interference impacts both the received signal at the relay, and the received signal at the destination. Interference alignment is a signaling technique that provides high multiplexing gain in the interference channel. In this paper, inspired by an algorithmic approach for interference alignment, three cooperative algorithms are proposed to find suboptimal solutions for end-to-end sum-rate maximization problem in a multiple-antenna amplify-and-forward (AF) relay interference channel. The first algorithm aims at minimizing the sum power of enhanced noise from the relays and interference at the receivers. The second and third algorithms aim at minimizing matrix-weighted sum mean square errors with either equality or inequality power constraints to utilize a connection between mean square error and mutual information. The resulting iterative algorithms are convergent to points that we conjecture to be stationary points of the corresponding problems. Simulations show that the proposed algorithms achieve higher end-to-end sum-rates and multiplexing gains that existing strategies for AF relays, decode-and-forward relays, and direct transmission. The first algorithm outperforms the other algorithms at high signal-to-noise ratio (SNR) but performs worse than them at low SNR. Thanks to power control, the third algorithm outperforms the second algorithm at the cost of additional overhead.