Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations

Abstract  Problems of best tensor product approximation of low orthogonal rank can be formulated as maximization problems on Stiefel
manifolds. The functionals that appear are convex and weakly sequentially continuous. It is shown that such problems are always
well-posed, even in the case of non-compact Stiefel manifolds. As a consequence, problems of finding a best orthogonal, strong
orthogonal or complete orthogonal low-rank tensor product approximation and problems of best Tucker format approximation to
any given tensor are always well-posed, even in spaces of infinite dimension. (The best rank-one approximation is a special
case of all of them.) In addition, the well-posedness of a canonical low-rank approximation with bounded coefficients can
be shown. The proofs are non-constructive and the problem of computation is not addressed here.

• Content Type Journal Article
• DOI 10.1007/s00211-009-0276-9
• Authors
  
  
  • André Uschmajew, Technische Universität Berlin Institut für Mathematik Straße des 17. Juni 136 10623 Berlin Germany
  
  

• Journal Numerische Mathematik
• Online ISSN 0945-3245
• Print ISSN 0029-599X

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Original source : http://www.springerlink.com/content/j7784356003044...