Distributed Nonconvex Optimization for Energy Efficiency in Mobile Ad Hoc Networks

This article proposes a distributed nonconvex optimization algorithm for energy efficiency (EE) in mobile ad hoc networks (MANETs). The proposed model for EE in MANETs can be classified into the category of nonconvex optimization problems. There are various distributed algorithms for solving nonconvex optimization problems. But, they are associated with some flaws such as complexity of implementation and low convergence rate. In this regard, in addition to the simplicity in implementation, the optimal point of the proposed model is a saddle point. Using augmented Lagrangian function with continuous-time optimization dynamics algorithm, a dynamic system will be established where its equilibrium points are Karush-Kuhn-Tucker points of the proposed model. Also, it will be shown that these points can be locally asymptotically stable under some conditions. Additionally, the proposed analytic method proves that the rate of convergence increases with an increasing penalty coefficient. To validate the performance of the presented algorithm, the problem of EE optimization for a sample mobile ad hoc network is simulated in MATLAB environment.