The weighted sum-rate maximization (WSRMax) problem plays a central role in many network control and optimization methods, such as power control, link scheduling, cross-layer control, network utility maximization. The problem is NP-hard in general.

This is a cohesive discussion of the existing solution methods associated with the WSRMax problem, including global, fast local, as well as decentralized methods is presented. In addition, general optimization approaches, such as branch and bound methods, complementary geometric programming, and decomposition methods, are discussed in depth to address the problem.

Through a number of numerical examples, the applicability of the resulting algorithms in various application domains is demonstrated. The presented algorithms and the associated numerical results can be very useful for network engineers or researchers with an interest in network design.