A wireless network of multiple transmitter-user pairs overheard by an eavesdropper, where the transmitters are equipped with multiple antennas, while the users and eavesdropper are equipped with a single antenna, is considered. At different levels of wireless channel knowledge, the problem of interest is beamforming to optimize the users' quality-of-service (QoS) in terms of their secrecy throughputs or maximize the network's energy efficiency under users' QoS. All these problems are seen as very difficult optimization problems with many nonconvex constraints and nonlinear equality constraints in beamforming vectors. The paper develops path-following computational procedures of low complexity and rapid convergence for the optimal beamforming solution. Their practicability is demonstrated through numerical examples.