With the rapid development of wireless sensor networks, reducing energy consumption is becoming one of the
important factors to extend node lifetime, and it is necessary to adjust the launching power of each node because
of the limited energy available to the sensor nodes in the networks. This paper proposes a power and rate control
model based on the network utility maximization (NUM) framework, where a weighting factor is used to reflect
the influence degree of the sending power and transmission rate to the utility function. In real networks, nodes
interfere with each other in the procedure of transmitting signal, which may lead to signal transmission failure
and may negatively have impacts on networks throughput. Using dual decomposition techniques, the NUM problem is
decomposed into two distributed subproblems, and then the conjugate gradient method is applied to solve the
optimization problem with the calculation of the Hessian matrix and its inverse in order to guarantee fast convergence
of the algorithm. The convergence proof is also provided in this paper. Numerical examples show that the proposed
solution achieves significant throughput compared with exiting approaches.