Self-duality and Maximal Angle of Proper Cones

Manu Mathew () and Chandrashekaran Arumugasamy ()
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Manu Mathew: Central University of Tamil Nadu
Chandrashekaran Arumugasamy: Central University of Tamil Nadu

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1177-1181

Abstract: Abstract It is known that a cone K in $$\mathbb {R}^n$$ R n is sub-dual if and only if the maximal angle of K is less than or equal to $$\frac{\pi }{2}$$ π 2 . Further, it is easy to verify that for a self-dual cone K, the maximal angle of K is $$\frac{\pi }{2}$$ π 2 . However, this condition is not sufficient. In this paper using the concepts of antipodal and critical pairs, we give a necessary and sufficient condition for a cone K in $$\mathbb {R}^n$$ R n to be self-dual. As a consequence, we observe that for a self-dual cone K, the set of all antipodal pairs, Nash pairs, critical pairs, and the complementarity set are the same and form an n-dimensional manifold.

Keywords: Antipodal pair; Critical pair; Nash pair proper cone; Self-duality; 52A40; 46N10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00832-3

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