Resumen de Critical angles between two convex cones II. Special cases

Alberto Seeger, David Sossa

• 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.