Critical angles between two convex cones II. Special cases

• Alberto Seeger ^[2] ; David Sossa ^[1]
  1. [1] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     
  2. [2] Université d’Avignon, Francia
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 24, Nº. 1, 2016, págs. 66-87
• Idioma: inglés
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• Resumen

  • The concept of critical angle between two linear subspaces has applications in statistics, numerical linear algebra and other areas. Such concept has been abundantly studied in the literature. Part I of this work is an attempt to build up a theory of critical angles for a pair of closed convex cones. The need of such theory is motivated, among other reasons, by some specific problems arising in regression analysis of cone-constrained data, see Tenenhaus in (Psychometrika 53:503–524, 1988). Angle maximization and/or angle minimization problems involving a pair of convex cones are at the core of our discussion. Such optimization problems are nonconvex in general and their numerical resolution offers a number of challenges. Part II of this work focusses on the practical computation of the maximal angle between specially structured cones.