This letter considers a sum-rate-maximizing power allocation problem under the Gaussian cognitive multiple-access channel (MAC), where primary users and secondary users may communicate under mutual interference. Formulating the problem as a standard nonconvex quadratically constrained quadratic problem (QCQP) provides a simple method to find a solution using semidefinite relaxation (SDR). Simulation results show that the solution achieves almost the same performance of the exhaustive search, within polynomial time.