Logo eprints

An SDP approach for l0-minimization: application to ARX model segmentation

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)

PDF (Pre-print version)
Download (161kB) | Preview


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.

Item Type: Article
Identification Number: 10.1016/j.automatica.2013.09.021
Funders: This work was supported by the Netherlands Organization for Scientific Research (NWO, grant. no.: 639.021.127) and by the French ministries of Foreign Affairs, Education and Research and the French-Dutch Academy (PHC Van Gogh project, n. 29342QL)
Uncontrolled Keywords: Compressive sensing; ℓ0ℓ0-minimization; Regularization; SDP relaxation; Sparse estimation; Segmentation
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 13 Jan 2015 14:18
Last Modified: 13 Jan 2015 14:18
URI: http://eprints.imtlucca.it/id/eprint/2474

Actions (login required)

Edit Item Edit Item