## Title data

Hintermüller, Michael ; Schiela, Anton ; Wollner, Winnifried:

**The length of the primal-dual path in Moreau-Yosida-based path-following methods for state constrained optimal control.**

*In:* SIAM Journal on Optimization.
Vol. 24
(2014)
Issue 1
.
- pp. 108-126.

ISSN 1095-7189

DOI: https://doi.org/10.1137/120866762

Review: |

## Project information

Project title: |
Project's official title Project's id DFG Research Center Matheon "Mathematics for key technologies" FZT 86 |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

A priori estimates of the length of the primal-dual path resulting from a Moreau-Yosida approximation of the feasible set for state constrained optimal control problems are derived. These bounds depend on the regularity of the state and the dimension of the problem. Numerical results indicate that the bounds are indeed sharp and are typically attained in cases where the active set consists of isolated active points. Further conditions on the multiplier approximation are identified which guarantee higher convergence rates for the feasibility violation due to the Moreau-Yosida approximation process. Numerical experiments show again that the results are sharp and accurately predict the convergence behavior.