The network lifetime for wireless sensor network plays an important role to survivability, Thus, we indicate the importance of routing protocol to network lifetime, and model the expected retransmission time as a convex function with respect to aggregate jlow on each sensor node. Thus we formulate the optimal energy-eficient routing as a non-linear min-max programming problem with convex productform, which can be optimally solved by optimal routing framework. Based on the optimal routing framework, we propose Lagrangean-based algorithm and primal optimal algorithm. By the combination of these two algorithms, we can optimally and efficiently get the routing assignment to maximize the network life in the sensor network. From experiments,we observe that when the optimal network lifetime increases as the number of sensor nodes increase. While the shortest path-based heuristic algorithm can only achieve about 48% network lifetime compared to our solution approach.