We develop a bioeconomic model to identify the cost-effective control of an invasive species (rain-bow trout) to achieve a population viability goal for an endangered species (humpback chub) in the Grand Canyon of the U.S. southwest. The population viability optimization problem is no-toriously difficult to solve due to a probabilistic restriction on joint outcomes (survival) over many periods. We develop a novel dynamic programming solution approach that is fast and forgoes the simulation method requirement of imposing structure on the policy function. We also investigate an adaptive management model that incorporates learning about uncertain bi-ological dynamics.