We propose a new parallel-in-time algorithm for solving optimal control problems constrained bypartial differential equations. Our approach, which is based on a deeper understanding of ParaExp,considers an overlapping time-domain decomposition in which we combine the solution of homogeneous problems using exponential propagation with the local solutions of inhomogeneous problems.The algorithm yields a linear system whose matrix-vector product can be fully performed in parallel.We then propose a preconditioner to speed up the convergence of GMRES in the special cases ofthe heat and wave equations. Numerical experiments are provided to illustrate the efficiency of ourpreconditioners.

翻译：本文提出了一种新的并行时间算法，用于求解偏微分方程约束下的最优控制问题。该方法基于对ParaExp算法的深入理解，采用重叠时间域分解策略，将齐次问题的指数传播解与非齐次问题的局部解相结合。该算法生成的线性系统，其矩阵-向量积运算可完全并行执行。针对热传导方程和波动方程这两种特殊情形，我们进一步提出了一种预条件子以加速GMRES迭代的收敛速度。数值实验验证了所提预条件子的有效性。