Approximate regularization path for nuclear norm based H2 model reduction
2014 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, 3637-3641 p.Conference paper (Refereed)
This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this tradeoff is determined by one crucial design parameter. The main contribution is a methodology to approximately calculate all solutions up to a certain tolerance to the model reduction problem as a function of the design parameter. This is called the regularization path in sparse estimation and is a very important tool in order to find the appropriate balance between fit and complexity. We extend this to the more complicated nuclear norm case. The key idea is to determine when to exactly calculate the optimal solution using an upper bound based on the so-called duality gap. Hence, by solving a fixed number of optimization problems the whole regularization path up to a given tolerance can be efficiently computed. We illustrate this approach on some numerical examples.
Place, publisher, year, edition, pages
IEEE conference proceedings, 2014. no February, 3637-3641 p.
IdentifiersURN: urn:nbn:se:kth:diva-176161DOI: 10.1109/CDC.2014.7039955ScopusID: 2-s2.0-84931863922OAI: oai:DiVA.org:kth-176161DiVA: diva2:874938
2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, 15 December - 17 December 2014
QC 201511302015-11-302015-11-022015-11-30Bibliographically approved