A nonsmooth primal-dual method with simultaneous adaptive PDE constraint solver

  title={A nonsmooth primal-dual method with simultaneous adaptive PDE constraint solver},
  author={Bj{\o}rn Jensen and Tuomo Valkonen},
We introduce an ecient rst-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this eciency through not solving the PDE or its linearisation on each iteration of the optimization method. Instead, we run the method in parallel 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… 

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