In this dissertation, I use mathematical optimization approach to solve the complex network problems. Paper l and paper 2 first show that ignoring the bandwidth constraint can lead to infeasible routing solutions. A sufficient condition on link bandwidth is proposed that makes a routing solution feasible, and then a mathematical optimization model based on this sufficient condition is provided. Simulation results show that joint optimization models can provide more feasible routing solutions and provide significant improvement on throughput and lifetime. In paper 3 and paper 4, an interference model is proposed and a transmission scheduling scheme is presented to minimize the end-to-end delay. This scheduling scheme is designed based on integer linear programming and involves interference modeling. Using this schedule, there are no conflicting transmissions at any time. Through simulation, it shows that the proposed link scheduling scheme can significantly reduce end-to-end latency. Since to compute the maximum throughput is an NP-hard problem, efficient heuristics are presented in Paper 5 that use sufficient conditions instead of the computationally-expensive-to-get optimal condition to capture the mutual conflict relation in a collision domain. Both one-way transmission and two-way transmission are considered. Simulation results show that the proposed algorithms improve network throughput and reduce energy consumption, with significant improvement over previous work on both aspects. Paper 6 studies the complicated tradeoff relation among multiple factors that affect the sensor network lifetime and proposes an adaptive multi-hop clustering algorithm. It realizes the best tradeoff among multiple factors and outperforms others that do not. It is adaptive in the sense the clustering topology changes over time in order to have the maximum lifetime --Abstract, page iv
