This paper presents a concurrent approach for solving dynamic programming optimization problems such as the generation of optimal cost-to-go functions for robot motion planning in dense environments. Such optimization techniques are core to many robotics problems, but traditional approaches are inherently impractical due to their computational complexity. This limitation usually results in a configuration space being subsampled, lower configuration space coverage, less frequent planner updates, or the use of sub-optimal graph-based road map methods. The proposed approach provides mathematically identical results to traditional grid-based motion planning solvers in at least an order of magnitude less time by leveraging the concurrent architecture found in modern graphics hardware. Although results given here are presented in a robot navigation context, they are also applicable to other dynamic programming problems. © 2014 Elsevier B.V. All rights reserved.