@article{eprints2474,
          number = {12},
          volume = {49},
          author = {Dario Piga and Roland T{\'o}th},
            year = {2013},
         journal = {Automatica},
           title = {An SDP approach for l0-minimization: application to ARX model segmentation },
           month = {December},
           pages = {3646 -- 3653},
       publisher = {Elsevier },
        keywords = {Compressive sensing; ?0?0-minimization; Regularization; SDP relaxation; Sparse estimation; Segmentation},
        abstract = {Abstract Minimizing the ? 0 -seminorm of a vector under convex constraints is a combinatorial (NP-hard) problem. Replacement of the ? 0 -seminorm with the ? 1 -norm is a commonly used approach to compute an approximate solution of the original ? 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 ? 1 -approximated problem is equal to the solution of the original ? 0 -minimization problem. However, the evaluation of the conservativeness of the ? 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 ? 0 -norm of a vector under given constraints. In particular, we show that an ? 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 ? 1 -based relaxation in detecting piece-wise constant parameter changes in the estimated model. },
             url = {http://eprints.imtlucca.it/2474/}
}