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This paper addresses the optimal cooperative beamforming design for multi-user multi-relay wireless networks in which the single-carrier frequency division multiple access (SC-FDMA) technique is employed at the terminals. The problem of interest is to find the beamforming weights across relays to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among source users subject to individual power constraints at each relay. Such a beamforming design is shown to be a hard nonconvex optimization problem and therefore it is mathematically challenging to find the optimal solution. By exploring its partial convex structures, we recast the design problem as minimization of a d.c. (difference of two convex) objective function subject to convex constraints and develop an effective iterative algorithm of low complexity to solve it. Simulation results show that our optimal cooperative beamforming scheme realizes the inherent diversity order of the relay network and it performs significantly better than the equal-power beamforming weights.