The rapid development from 4G to 5G of mobile communications poses significant challenges in providing high rate and capacity, making it more crucial for efficient utilization of time-frequency resource via optimally configuring the network. Mathematical optimization serves as a powerful tool for addressing this type of problems. However, gauging its potential in large-scale cellular networks is non-trivial due to the inherent coupling relation of interference among cells. To address this issue, the dissertation adopts a so-called load-coupling system that mathe-matically formulates the mutual influence caused by radio resource allocation among cells. The model defines the time-frequency resource consumption in each cell as the cell load. The load of one cell governs the interference that the cell generates to the others, since the cell trans-mits more frequently with higher load. The model enables joint optimization of resource al-location in multiple cells with respect to the dynamics of resource occupancy of cells. Under the load coupling model, the dissertation applies mathematical optimization to resolve resource management problems with respect to a number of evolving technologies, such as coordinated multipoint (CoMP) transmission, wireless relays, cloud radio access networks (C-RAN), and non-orthogonal multiple access (NOMA). Six research papers are included in the dissertation. Paper I addresses the question of how network planning and coordination may increase the ef-ficiency of spectrum usage, by jointly optimizing user association and resource allocation with CoMP. Paper II investigates the potential of relay cooperation for energy saving. As an extension of Paper I, Paper III studies the capacity maximization for a target group of users, while keep-ing the quality-of-service (QoS) of other users being strictly met. Paper IV provides a general framework and a series of theoretical analysis for algorithmically enabling resource optimization in multi-cell NOMA with load coupling, where users are allowed to group together for sharing time-frequency resource by successive interference cancellation (SIC). Under this framework, Paper V explores the potential of NOMA networks. For a restricted setup of NOMA, the paper achieves globally optimal resource usage efficiency, in terms of power allocation, user pair se-lection, and time-frequency resource allocation. Finally, Paper VI, serving as a complementary note, overcomes a key obstacle in analyzing convergence of applying load coupling in NOMA networks.