Abstract
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.
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D. Sossa is supported by CONICYT, Chile.
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Seeger, A., Sossa, D. Critical angles between two convex cones II. Special cases. TOP 24, 66–87 (2016). https://doi.org/10.1007/s11750-015-0382-z
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DOI: https://doi.org/10.1007/s11750-015-0382-z
Keywords
- Nonconvex optimization
- Maximal angle
- Critical angle
- Convex cones
- Topheavy cones
- Ellipsoidal cones
- Cones of matrices