Mesh Refinement with Early Termination for Dynamic Feasibility Problems
<|reference_start|>Mesh Refinement with Early Termination for Dynamic Feasibility Problems: We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an infinite-dimensional problem into a sequence of finite-dimensional optimization subproblems. Each subproblem in the sequence is a finer approximation of the previous. It is shown that these subproblems need not be solved to a high precision; instead, an early termination procedure can determine when mesh refinement should be performed. The new refinement strategy, applied to an inverted pendulum swing-up problem, outperforms a conventional refinement method by up to a factor of three in function evaluations.<|reference_end|>
@article{vila2024mesh,
    title={Mesh Refinement with Early Termination for Dynamic Feasibility Problems},
    author={Eduardo M. G. Vila, Eric C. Kerrigan and Paul Bruce},
    journal={IFAC-PapersOnLine Volume 56, Issue 2, 2023, Pages 10576-10581},
    year={2024},
    doi={10.1016/j.ifacol.2023.10.676},
    archivePrefix={arXiv},
    eprint={2403.07811},
    primaryClass={math.OC cs.SY eess.SY}
}