Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The state-of-the-art parallel preconditioner for linear problems leads to a set of independent smaller systems that are currently hard to solve. We generalize the preconditioner to the nonlinear case and propose a new, fast inversion method for these smaller systems, avoiding disadvantages of the current options with adjusted boundary conditions in the subproblems.

翻译：最近，ParaOpt算法作为时间并行Parareal方法在最优控制领域的扩展被提出。ParaOpt采用拟牛顿迭代步，每一步都需要迭代求解匹配条件方程组。针对线性问题的最先进并行预条件子会导出一组独立的较小规模方程组，这些方程组目前难以高效求解。本文将预条件子推广至非线性情形，并提出一种针对这些较小系统的新型快速反演方法，避免了现有方案中通过调整子问题边界条件所带来的缺陷。