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For wireless ad hoc networks with random access, we propose an optimal rate allocation and power control mechanism. First, a network utility maximization problem and an energy minimization problem are given in this paper. Using multiobjective optimization theory, we then combine the two conflicting optimization problem together into a new optimization problem. Finally, the new optimization problem is vertically decomposed into three subproblems with the Lagrange dual decomposition: a rate allocation problem at the transport layer, a contention resolution problem at the medium access control (MAC) layer and a power control problem at the physical layer. We prove rigorously that the proposed algorithm can converge quickly. Theoretical analysis and simulation results are provided in support of our conclusions.