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Energy-efficient routing is a critical problem in multihop wireless networks due to the severe power constraint of wireless nodes. Despite its importance and many research efforts toward it, a distributed routing algorithm that maximizes network lifetime is still missing. To address this problem, this paper proposes a novel utility-based nonlinear optimization formulation to the maximum lifetime routing problem. Based on this formulation, a fully distributed localized routing algorithm is further presented, which is proved to converge at the optimal point, where the network lifetime is maximized. Solid theoretical analysis and simulation results are presented to validate the proposed solution. [ABSTRACT FROM AUTHOR]