Confexifying the Counting Function on ℝ^p for Convexifying the Rank Function on ℳ_{m,n}(ℝ)

Abstract

We calculate the convex hull of the so-called counting function restricted to a ball of

\mathbb{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

\mathcal{M}_{m,n}(\mathbb{R})

, the space of real (m,n)-matrices.

Contact details are reproduced from the original publication and may be historical.

Institut de Mathématiques, Université P. Sabatier, 118, route de Narbonne, 31062 Toulouse, France

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.