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Computing Critical Angles Between Two Convex Cones

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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.

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Acknowledgements

The authors acknowledge the support of MATH-AMSUD 23-MATH-09 MORA-DataS project. The research of V. Sessa and W. de Oliveira benefited from the support of the Gaspard-Monge Program for Optimization and Operations Research (PGMO) project “SOLEM - Scalable Optimization for Learning and Energy Management”. D. Sossa is partially supported by FONDECYT (Chile) through grant 11220268.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées (CMA), Mines Paris, Université PSL, Sophia Antipolis, Paris, France

    Welington de Oliveira & Valentina Sessa

  2. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Av. Libertador Bernardo O’Higgins 611, Rancagua, Chile

    David Sossa

Authors
  1. Welington de Oliveira
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  2. Valentina Sessa
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  3. David Sossa
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Correspondence to David Sossa.

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Communicated by Radu Ioan Bot.

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de Oliveira, W., Sessa, V. & Sossa, D. Computing Critical Angles Between Two Convex Cones. J Optim Theory Appl 201, 866–898 (2024). https://doi.org/10.1007/s10957-024-02424-3

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