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Because the energy consumption is growing rapidly, green radio, which lays emphasis on the energy efficiency (EE) in wireless networks, is becoming increasingly important. As potential paradigms for future wireless network design, cognitive radio (CR) is a promising technology to solve the spectrum shortage and inefficiency issues, while cooperative relay is capable of improving spectral efficiency by combating severe fading in wireless environment. In this paper, we investigate the energy-efficient power allocation problem in orthogonal frequency division multiplexing (OFDM)-based relaying CR networks. We develop a general framework to maximize the overall EE of the CR system, under the constraints of transmission power budget, traffic demands, and the interference constraints of the primary users. Our problem formulation is a nonconvex optimization task, and it is hard to obtain the optimal solution. We first convert our formulated problem into a convex optimization problem via its hypograph form, which can be solved by the barrier method. Then we further speed up the computation of Newton step during the barrier method, significantly reducing the complexity of the algorithm by exploiting its special structure. Numerical results validate that our method can exploit the overall EE of CR systems, while the algorithm converges efficiently and stably. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]