relation: http://eprints.imtlucca.it/2474/
title: An SDP approach for l0-minimization: application to ARX model segmentation 
creator: Piga, Dario
creator: Tóth, Roland
subject: QA75 Electronic computers. Computer science
description: Abstract Minimizing the ℓ 0 -seminorm of a vector under convex constraints is a combinatorial (NP-hard) problem. Replacement of the ℓ 0 -seminorm with the ℓ 1 -norm is a commonly used approach to compute an approximate solution of the original ℓ 0 -minimization problem by means of convex programming. In the theory of compressive sensing, the condition that the sensing matrix satisfies the Restricted Isometry Property (RIP) is a sufficient condition to guarantee that the solution of the ℓ 1 -approximated problem is equal to the solution of the original ℓ 0 -minimization problem. However, the evaluation of the conservativeness of the ℓ 1 -relaxation approaches is recognized to be a difficult task in case the {RIP} is not satisfied. In this paper, we present an alternative approach to minimize the ℓ 0 -norm of a vector under given constraints. In particular, we show that an ℓ 0 -minimization problem can be relaxed into a sequence of semidefinite programming problems, whose solutions are guaranteed to converge to the optimizer (if unique) of the original combinatorial problem also in case the {RIP} is not satisfied. Segmentation of {ARX} models is then discussed in order to show, through a relevant problem in system identification, that the proposed approach outperforms the ℓ 1 -based relaxation in detecting piece-wise constant parameter changes in the estimated model. 
publisher: Elsevier 
date: 2013-12
type: Article
type: PeerReviewed
format: application/pdf
language: en
identifier: http://eprints.imtlucca.it/2474/1/Aut2013PigaPreprint2.pdf
identifier:   Piga, Dario and Tóth, Roland  An SDP approach for l0-minimization: application to ARX model segmentation.  Automatica, 49 (12).  3646 - 3653.  ISSN 0005-1098      (2013)  
relation: http://www.sciencedirect.com/science/article/pii/S0005109813004548
relation: 10.1016/j.automatica.2013.09.021