Authors: | Stošić, Marko Marques, Manuel Costeira, João Paulo |
Title: | Convex solution of a permutation problem | Journal: | Linear Algebra and Its Applications | Volume: | 434 | Issue: | 1 | First page: | 361 | Last page: | 369 | Issue Date: | 1-Jan-2011 | Rank: | M22 | ISSN: | 0024-3795 | DOI: | 10.1016/j.laa.2010.08.028 | Abstract: | In this paper, we show that a problem of finding a permuted version of k vectors from RN such that they belong to a prescribed rank r subset, can be solved by convex optimization. We prove that under certain generic conditions, the wanted permutation matrix is unique in the convex set of doubly-stochastic matrices. In particular, this implies a solution of the classical correspondence problem of finding a permutation that transforms one collection of points in Rk into the another one. Solutions to these problems have a wide set of applications in Engineering and Computer Science. |
Keywords: | Convex optimization | Doubly-stochastic matrices | Permutation | Perron-Frobenius theorem | Publisher: | Elsevier | Project: | FCT project PRINTART PTDC/EEA - CRO/098822/2008 |
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