We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the forward-backward structure of the optimality system. Variants can be found using only Dirichlet and Neumann transmission conditions. Some of these variants are only good smoothers, while others could lead to efficient solvers.

翻译：本文针对无约束抛物型最优控制问题，提出了结合时间域分解的经典Schwarz方法。与Dirichlet-Neumann及Neumann-Neumann算法不同，我们基于最优性系统的前向-后向结构发现了不同的特性。通过仅使用Dirichlet和Neumann传输条件，可以衍生出多种变体方法。其中部分变体仅具备良好的平滑效果，而其他变体则可能发展为高效求解器。