New publication in Journal of Optimization Theory and Applications :

Computing Critical Angles Between Two Convex Cones

By Welington DE OLIVEIRA, Valentina SESSA and David SOSSA

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.

Citation: de Oliveira, W., Sessa, V. Sossa, D. Computing Critical Angles Between Two Convex Cones. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02424-3