A nonsmooth primal-dual method with interwoven PDE constraint solver
Jensen, B., & Valkonen, T. (2024). A nonsmooth primal-dual method with interwoven PDE constraint solver. Computational Optimization and Applications, Early online. https://doi.org/10.1007/s10589-024-00587-3
Julkaistu sarjassa
Computational Optimization and ApplicationsPäivämäärä
2024Tekijänoikeudet
© The Author(s) 2024
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.
Julkaisija
SpringerISSN Hae Julkaisufoorumista
0926-6003Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/220430934
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Lisätietoja rahoituksesta
Open Access funding provided by University of Helsinki (including Helsinki University Central Hospital). This research has been supported by the Academy of Finland Grants 314701, 320022, and 345486.Lisenssi
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