Computing Critical Angles Between Two Convex Cones

Welington Oliveira, Valentina Sessa and David Sossa ()
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Welington Oliveira: Mines Paris, Université PSL
Valentina Sessa: Mines Paris, Université PSL
David Sossa: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 2, No 14, 866-898

Abstract: Abstract This paper addresses the numerical computation of critical angles between two convex cones in Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary points of a fractional programming problem. To efficiently compute these stationary points, we introduce a partial linearization-like algorithm that offers significant computational advantages. Solving a sequence of strictly convex subproblems with straightforward solutions in several settings gives the proposed algorithm high computational efficiency while delivering reliable results: our theoretical analysis demonstrates that the proposed algorithm asymptotically computes critical angles. Numerical experiments validate the efficiency of our approach, even when dealing with problems of relatively large dimensions: only a few seconds are necessary to compute critical angles between different types of cones in spaces of dimension 1000.

Keywords: Critical angle; Convex cone; Fractional programming; Optimality conditions; Euclidean Jordan algebra; 52A40; 90C26; 90C32; 90C46; 17C99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02424-3

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