Inexact Restoration and Adaptive Mesh Refinement for Constrained Optimal Control

A new adaptive mesh refinement algorithm is proposed for solving Euler discretization of stateand control-constrained optimal control problems. Our approach is designed to reduce the computational effort by applying the inexact restoration (IR) method, a numerical method for nonlinear programming problems, in an innovative way. The initial iterations of our algorithm start with a coarse mesh, which typically involves far fewer discretization points than the fine mesh over which we aim to obtain a solution. The coarse mesh is then refined adaptively, by using the sufficient conditions of convergence of the IR method. The resulting adaptive mesh refinement algorithm is convergent to a fine mesh solution, by virtue of convergence of the IR method. We illustrate the algorithm on a computationally challenging constrained optimal control problem involving a container crane. Numerical experiments demonstrate that significant computational savings can be achieved by the new adaptive mesh refinement algorithm over the fixed-mesh algorithm. Conceivably owing to the small number of variables at the start, the adaptive mesh refinement algorithm appears to be more robust as well, i.e., it can find solutions with a much wider range of initial guesses, compared to the fixed-mesh algorithm.