Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization

@article{Clason2017PrimalDualEM,
  title={Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization},
  author={Christian Clason and T. Valkonen},
  journal={SIAM J. Optim.},
  year={2017},
  volume={27},
  pages={1314-1339}
}
  • Christian Clason, T. Valkonen
  • Published 2017
  • Mathematics, Computer Science
  • SIAM J. Optim.
  • We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity of the corresponding primal-dual optimality conditions. We also show convergence for a Nesterov-type accelerated variant provided one part of the functional is strongly convex. We show the applicability of the accelerated algorithm to examples of inverse… CONTINUE READING
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