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The cosine measure relative to a subspace

Author

Listed:
  • Charles Audet

    (Polytechnique Montréal)

  • Warren Hare

    (University of British Columbia)

  • Gabriel Jarry-Bolduc

    (Mount Royal University)

Abstract

The cosine measure was introduced in 2003 to quantify the richness of finite positive spanning sets of directions in the context of derivative-free directional methods. A positive spanning set is a set of vectors whose nonnegative linear combinations span the whole space. The present work extends the definition of cosine measure. In particular, the paper studies cosine measures relative to a subspace, and proposes a deterministic algorithm to compute it. The paper also studies the situation in which the set of vectors is infinite. The extended definition of the cosine measure might be useful for subspace decomposition methods.

Suggested Citation

  • Charles Audet & Warren Hare & Gabriel Jarry-Bolduc, 2025. "The cosine measure relative to a subspace," Computational Optimization and Applications, Springer, vol. 92(1), pages 125-153, September.
    • Handle: RePEc:spr:coopap:v:92:y:2025:i:1:d:10.1007_s10589-025-00701-z
    DOI: 10.1007/s10589-025-00701-z
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    References listed on IDEAS

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    1. Rommel G. Regis, 2021. "On the properties of the cosine measure and the uniform angle subspace," Computational Optimization and Applications, Springer, vol. 78(3), pages 915-952, April.
    2. S. Gratton & C. W. Royer & L. N. Vicente & Z. Zhang, 2019. "Direct search based on probabilistic feasible descent for bound and linearly constrained problems," Computational Optimization and Applications, Springer, vol. 72(3), pages 525-559, April.
    3. David Kozak & Stephen Becker & Alireza Doostan & Luis Tenorio, 2021. "A stochastic subspace approach to gradient-free optimization in high dimensions," Computational Optimization and Applications, Springer, vol. 79(2), pages 339-368, June.
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