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Dr. Nils Langenberg
- Contact:
FB 4 - Mathematics
University of Trier
54286 Trier, Germany
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E-mail address:
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nl-mathematics"at"t-online.de
I am no longer able to receive mails via langenberg@uni-trier.de. |
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In 2011 I obtained my PhD degree (Dr. rer. nat.) at Trier University; the examination board consisted of Ekkehard W. Sachs (head), Rainer Tichatschke (advisor) and Sjur Didrik Flam (external referee).
Research
Interests
My research interests essentially cover solution methods for variational inequalities, equilibrium problems and related issues. In particular, the focus is put on extensions of the Proximal Point Algorithm, especially interior proximal methods, the Auxiliary Problem Principle and extragradient methods. There is also a certain interest in topics from nonlinear optimization, convex analysis as well as generalized convexity and generalized monotonicity.
Publications
Peer reviewed publications
Langenberg, N.: Interior Proximal Method Without the Cutting Plane Property.
Journal of
Optimization Theory and Applications (JOTA), not yet assigned to an issue. Langenberg, N.: Interior proximal extragradient method for equilibrium
problems.
Optimization, not yet assigned to an issue. Langenberg, N.: An
interior proximal method for a class of quasimonotone
variational inequalities.
Journal of
Optimization Theory and Applications (JOTA), Volume 155, Issue
3 (2012), 902-922. Langenberg, N.: Interior
point methods for equilibrium problems.
Computational
Optimization and Applications, Volume 53, Issue 2 (2012),
453-483. Langenberg, N.: Convergence
of proximal-like methods for variational inequalities and fixed
point problems. Applications to the Nash equilibrium
problem.
Dissertation, University of Trier.
Published as a book at Logos Verlag Berlin, ISBN
978-3-8325-2890-4, 256 pages.
Langenberg, N.: Interior
proximal methods for equilibrium programming. Part
II.
Optimization, Volume 62, Issue 12 (2013), 1603-1625. Langenberg, N.: Interior
proximal methods for equilibrium programming. Part
I.
Optimization, Volume 62, Issue 9 (2013), 1247-1266. Langenberg, N. and Tichatschke, R.:
Interior
proximal methods for quasiconvex optimization.
Journal
of Global Optimization, Volume 52, Issue 3 (Special Issue
dedicated to Reiner Horst, 2012), 641-661.
Langenberg, N.: On
the cutting plane property and the Bregman Proximal Point
Algorithm.
Journal of Convex Analysis, Volume
18, Issue 3 (2011), 601-619. Langenberg, N.: Convergence
analysis of an Extended Auxiliary Problem Principle with
various stopping criteria.
Optimization Methods
and Software, Volume 26, Issue 1 (2011), 127-154. Langenberg, N.: Pseudomonotone
Operators and the Bregman Proximal Point Algorithm.
Journal
of Global Optimization, Volume 47, Issue 4 (2010), 537-555.
Other, partly reviewed publications
Langenberg, N.: Extended Proximal
Auxiliary Problem Principle for variational inequalities:
Convergence and numerical results for different stopping
criteria.
Poster, September 2009.
Langenberg, N.: On proximal-like
methods for equilibrium programming.
Technical Report
09-4, University of Trier, Germany, 2009. Langenberg, N.: Convergence analysis
of an extended Auxiliary Problem Principle for solving
variational inequalities.
Technical Report 08-8,
University of Trier, Germany, 2008. Langenberg, N.: Über zwei
Methoden zur Lösung von Variationsungleichungen.
Diploma
thesis, University of Trier, Germany, 2007.
Referee activities
I have acted as a referee in the peer review process for the following journals at least once (alphabetical order):
- Algorithms
- Applied Mathematics Letters
- European Journal of Operational Research
- Journal of Applied Mathematics and Computing
- Journal of Global Optimization
- Numerical Functional Analysis and Optimization
- Optimization
- Optimization Letters
- Optimization Methods & Software
- SIAM Journal on Optimization
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