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The authors consider the problem of joint routing, scheduling and power control in multi-hop wireless networks. They use a linear relation between link capacity and signal to interference noise ratio in their formulation. In a previous work, using a duality approach, the optimal link scheduling and power control that minimizes the total average transmission power is found. They formulate this problem as a linear programming problem with exponential number of constraints. To cope with the exponential number of constraints, they propose an iterative algorithm based on the cutting plane method. The separation Oracle for the cutting plane algorithm turns out to be an element-wise concave optimization problem that can be effectively solved using branch and bound algorithm.
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