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In wireless networks, power allocation is an effective technique for prolonging network lifetime, achieving better quality-of-service (QoS), and reducing network interference. However, these benefits depend on knowledge of the channel state information (CSI), which is hardly perfect. Therefore, robust algorithms that take into account such CSI uncertainties play an important role in the design of practical systems. In this paper, we develop relay power allocation algorithms for noncoherent and coherent amplify-and-forward (AF) relay networks. The goal is to minimize the total relay transmission power under individual relay power constraints, while satisfying a QoS requirement. To make our algorithms practical and attractive, our power update rate is designed to follow large-scale fading, i.e., in the order of seconds. We show that, in the presence of perfect global CSI, our power optimization problems for noncoherent and coherent AF relay networks can be formulated as a linear program and a second-order cone program (SOCP), respectively. We then introduce robust optimization methodology that accounts for uncertainties in the global CSI. In the presence of ellipsoidal uncertainty sets, the robust counterparts of our optimization problems for noncoherent and coherent AF relay networks are shown to be an SOCP and a semi-definite program, respectively. Our results reveal that ignoring uncertainties associated with global CSI often leads to poor performance. We verify that our proposed algorithms can provide significant power savings over a naive scheme that employs maximum transmission power at each relay node. This work highlights the importance of robust algorithms with practical power update rates in realistic wireless networks.