论文标题
用交织PDE约束求解器的非平滑原始偶对偶的方法
A nonsmooth primal-dual method with interwoven PDE constraint solver
论文作者
论文摘要
我们引入了一种有效的一阶原始偶对偶，以解决非平滑PDE受限优化问题的解决方案。我们通过不求解PDE或在优化方法的每种迭代中实现这种效率。取而代之的是，我们运行该方法与简单的常规线性系统求解器（Jacobi，Gauss-seidel，coogate梯度）交织在一起，对于优化方法的每个步骤，始终仅比线性系统求解器一步一步。根据优化方法确定的每个迭代对控制参数进行更新。我们证明在二阶生长条件下线性收敛，并在数值上证明了与涉及边界测量的各种PDE的性能。
We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization method. Instead, we run the method interwoven with a simple conventional linear system solver (Jacobi, Gauss-Seidel, conjugate gradients), always taking only one step of the linear system solver for each step of the optimization method. The control parameter is updated on each iteration as determined by the optimization method. We prove linear convergence under a second-order growth condition, and numerically demonstrate the performance on a variety of PDEs related to inverse problems involving boundary measurements.
