We consider the problem of secrecy rate maximization in a multi-input multi-output multi-eavesdropper (MIMOME) wiretap channel and present an exact solution. A general system model with a multi-antenna eavesdropper and a multi-antenna full-duplex receiver is considered. In particular, we perform joint beamforming and artificial noise optimization in an effort to maximize the achievable secrecy rate. The optimization is performed in the presence of artificial noise generated by both transmitter and legitimate receiver. The resulting optimization problem is non-convex and difficult to solve. We develop a minorization-maximization algorithm to solve the problem. It is iterative in nature and guaranteed to converge to a locally optimal solution. The results can therefore be used to benchmark existing methods. Numerical results are presented to demonstrate the efficacy of the proposed approach.