On angles between convex cones
نویسندگان
چکیده
There are two basic angles associated with a pair of linear subspaces: the Diximier angle and Friedrichs angle. These classical notions, which date back to first half 20th century, have been thoroughly studied due their utility in description convergence rates for various projection-based algorithms solving feasibility problems. The Dixmier orthogonal complements is same as original provided that gives rise direct (not necessarily orthogonal) sum underlying Hilbert space. Even more satisfyingly, always coincide. beautiful results Krein, Krasnoselskii, Milman Solmon, respectively. In 1995, Deutsch very nice survey complete proofs interesting historical comments. One key result Deutsch's was an inequality by Hundal. In this paper, we present extensions these case when subspaces only required be convex cones. It turns out Hundal's has conical extension while situation technical Krein et al. Solmon. Our analysis based on our recent work between sets. Throughout, also provide examples illustrating sharpness results.
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ژورنال
عنوان ژورنال: Journal of applied and numerical optimization
سال: 2022
ISSN: ['2562-5527', '2562-5535']
DOI: https://doi.org/10.23952/jano.4.2022.2.02