The cosine measure relative to a subspace

Charles Audet (), Warren Hare () and Gabriel Jarry-Bolduc ()
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Charles Audet: Polytechnique Montréal
Warren Hare: University of British Columbia
Gabriel Jarry-Bolduc: Mount Royal University

Computational Optimization and Applications, 2025, vol. 92, issue 1, No 4, 125-153

Abstract: 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.

Keywords: Positive spanning set; Positive basis; Cosine measure; Gradient approximation; Subspace decomposition (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00701-z

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