We propose a novel direct transcription and solution method for solving
nonlinear, continuous-time dynamic optimization problems. Instead of forcing
the dynamic constraints to be satisfied only at a selected number of points as
in direct collocation, the new approach alternates between minimizing and
constraining the squared norm of the dynamic constraint residuals integrated
along the whole solution trajectories. As a result, the method can 1) obtain
solutions of higher accuracy for the same mesh compared to direct collocation
methods, 2) enables a flexible trade-off between solution accuracy and
optimality, 3) provides reliable solutions for challenging problems, including
those with singular arcs and high-index differential algebraic equations.