PDE-Constrained Optimization Subject to Pointwise Constraints on the Control, the State, and Its Derivative

@article{Hintermller2009PDEConstrainedOS,
  title={PDE-Constrained Optimization Subject to Pointwise Constraints on the Control, the State, and Its Derivative},
  author={Michael Hinterm{\"u}ller and Karl Kunisch},
  journal={SIAM Journal on Optimization},
  year={2009},
  volume={20},
  pages={1133-1156}
}
A general Moreau–Yosida-based framework for minimization problems subject to partial differential equations and pointwise constraints on the control, the state, and its derivative is considered. A range space constraint qualification is used to argue existence of Lagrange multipliers and to derive a KKT-type system for characterizing first-order optimality of the unregularized problem. The theoretical framework is then used to develop a semismooth Newton algorithm in function space and to prove… CONTINUE READING
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