Confexifying the Counting Function on R<sup>p</sup> for Convexifying the Rank Function on M<sub>m,n</sub>(R)

H. Y. Le

Geodesic

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Confexifying the Counting Function on R^p for Convexifying the Rank Function on M_m,n(R)

H. Y. Le

Journal of convex analysis, Tome 19 (2012) no. 2, pp. 519-524.

Voir la notice de l'article provenant de la source Heldermann Verlag

Résumé

We calculate the convex hull of the so-called counting function restricted to a ball of R^p, and we then use it, with a result of A. Lewis, to recover the convex hull of the rank function restricted to a ball of M_m,n(R), the space of real (m,n)-matrices.

Mots-clés : Counting function, convex hull, rank of a matrix

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     author = {H. Y. Le},
     title = {Confexifying the {Counting} {Function} on {R\protect\textsuperscript{p}} for {Convexifying} the {Rank} {Function} on {M\protect\textsubscript{m,n}(R)}},
     journal = {Journal of convex analysis},
     pages = {519--524},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a10/}
}

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H. Y. Le. Confexifying the Counting Function on R^p for Convexifying the Rank Function on M_m,n(R). Journal of convex analysis, Tome 19 (2012) no. 2, pp. 519-524. http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a10/