Joint Transmission Power Optimization and Connectivity Control in Asymmetric Networks
Milad Esmaeilpour, Amir G. Aghdam, Stéphane Blouin · 2018
In this paper, the problem of transmission power optimization and connectivity control over asymmetric networks represented by weighted directed graphs (digraphs) is investigated using a centralized approach. The notion of generalized algebraic connectivity (GAC) introduced in the literature recently as a measure of connectivity in weighted digraphs is formulated as an implicit function of the network's transmission power vector. An optimization problem is then presented to minimize the total transmission power of the network while satisfying certain constraints on the GAC and transmission power. The interior point method is used to transform this constrained optimization problem into a sequential unconstrained optimization problem. Each subproblem is then solved numerically using the subgradient method with backtracking line search. Even though the GAC is a non-convex and non-differentiable continuous function of the network's transmission power vector, using the aforementioned methods the optimization problem gradually becomes convex as the number of iterations increases. Asymptotic convergence of the proposed algorithm to the global minimum of the original optimization problem is demonstrated analytically. The effectiveness of the algorithm is verified by simulations.