© 2014 IEEE. This paper presents an algorithm for minimizing the execution time of a geometric robot path while satisfying dynamic force and torque constraints. The formulation is numerically stable, using a convex optimization that is guaranteed to converge to a unique optimum, and it is also scalable due to the use of a fast feasible set precomputation step that greatly reduces dimensionality of the optimization problem. The algorithm handles frictional contact constraints with arbitrary numbers of contact points as well as torque, acceleration, and velocity limits. Results are demonstrated in simulation on locomotion problems on the Hubo-II+ and ATLAS humanoid robots, demonstrating that the algorithm can optimize trajectories for robots with dozens of degrees of freedom and dozens of contact points in a few seconds.