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We consider the energy-efficient network resource allocation that minimizes a cost function of average user powers for multi-hop wireless networks. A class of fair cost functions is derived to balance the tradeoff between efficiency and fairness in energy-efficient designs. Based on such cost functions, optimal routing, scheduling and power control schemes are developed. Relying on stochastic optimization tools, we further develop stochastic network resource allocation schemes which are capable of dynamically learning the traffic and channel statistics, and converging to the optimal strategy on-the-fly.