The Primal-Dual Active Set Strategy as a Semismooth Newton Method

@article{Hintermller2002ThePA,
  title={The Primal-Dual Active Set Strategy as a Semismooth Newton Method},
  author={Michael Hinterm{\"u}ller and Kazufumi Ito and Karl Kunisch},
  journal={SIAM J. Optim.},
  year={2002},
  volume={13},
  pages={865-888}
}
This paper addresses complementarity problems motivated by constrained optimal control problems. It is shown that the primal-dual active set strategy, which is known to be extremely efficient for this class of problems, and a specific semismooth Newton method lead to identical algorithms. The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept. This leads to new local… 

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