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

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 1052-6234
DOI: https://doi.org/10.1137/120866762

Review:

Official URL: Volltext

Project information

Project title:
Project's official titleProject'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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: Preliminary versions are published in ZIB Report 11-37 (2011) and in Hamburger Beiträge zur Angewandten Mathematik 2012-03 (2012).
Keywords: Moreau-Yosida regularization; PDE constrained optimization; path-following; pointwise state constraints; regularization error
Subject classification: Mathematics Subject Classification Code: 49M30 (49J52 49J20)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 02 Feb 2015 15:15
Last Modified: 19 Mar 2015 11:48
URI: https://eref.uni-bayreuth.de/id/eprint/6116