Lifetime Optimization and Connectivity Control in Asymmetric Networks

The problem of lifetime maximization and connectivity control in an asymmetric network is considered in this work. It is assumed that the network is modeled by a weighted directed graph, and that the information flow structure is centralized. The generalized algebraic connectivity notion is adopted as the network connectivity measure, and is formulated here as an implicit function of the transmission powers used by the nodes to communicate with their neighbors. An optimization problem is presented to maximize the network lifetime while ensuring that the degree of connectivity of the network is above a prespecified threshold and that transmission powers of the nodes are limited to a predefined range. The mixed interior point-exterior point technique is utilized to convert the problem into a sequential unconstrained optimization. In order to solve each subproblem numerically in the new framework, the subgradient technique with backtracking line search is utilized. It is shown that the proposed solution asymptotically converges to the global optimum of the original optimization problem. Simulations confirm the efficacy of the proposed technique.