This chapter explores the application of semidefinite programming (SDP) to solve the optimal power flow (OPF) problem in monopolar multiterminal high-voltage direct current (MT-HVDC) systems. By leveraging the convex relaxation capabilities of SDP, the inherently non-convex OPF problem is transformed into a convex framework, ensuring computational efficiency and global optimality. The chapter presents the theoretical foundations of SDP, details the reformulation of the OPF problem using matrix-based decision variables, and demonstrates the use of SDP to optimize power generation, minimize power losses, and maintain voltage stability. Numerical validations on an 11-node MT-HVDC test system highlight the method’s effectiveness in maintaining voltages within acceptable limits, achieving balanced power generation, and minimizing system losses. The results also confirm the efficient distribution of line currents, ensuring operational safety and thermal compliance. This study underscores the versatility and robustness of SDP as a critical tool for addressing complex, large-scale optimization problems in modern power systems, particularly in networks with renewable energy integration and dynamic operational conditions.