Biblio

Although beamforming optimization problems in full-duplex communication systems can be optimally solved with the semidefinite relaxation (SDR) approach, its computational complexity increases rapidly when the problem size increases. In order to circumvent this issue, in this paper, we propose an alternating direction of multiplier method (ADMM) which minimizes the augmented Lagrangian of the dual of the SDR and handles the inequality constraints with the use of slack variables. The proposed ADMM is then applied for optimizing the relay beamformer to maximize the secrecy rate. Simulation results show that the proposed ADMM performs as good as the SDR approach.

Distributed optimization is an emerging research topic. Agents in the network solve the problem by exchanging information which depicts people's consideration on a optimization problem in real lives. In this paper, we introduce two algorithms in continuous-time to solve distributed optimization problems with equality constraints where the cost function is expressed as a sum of functions and where each function is associated to an agent. We firstly construct a continuous dynamic system by utilizing the Lagrangian function and then show that the algorithm is locally convergent and globally stable under certain conditions. Then, we modify the Lagrangian function and re-construct the dynamic system to prove that the new algorithm will be convergent under more relaxed conditions. At last, we present some simulations to prove our theoretical results.