EURO Journal on Computational Optimization· 2026Q2
On the computation of cosine measures in high dimensions
- 0citations
- Q2SCImago
- 2026year
Short summary
New heuristics and a formulation are proposed to compute the cosine measure in high-dimensional derivative-free optimization (DFO), a problem recently shown to be NP-hard.
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Key points
- The cosine measure computation in high-dimensional DFO is NP-hard.
- New heuristics and a formulation are proposed to tackle this problem.
- New theoretical results allow for the construction of sets with prescribed cosine measures.
- The proposed algorithms are compared against existing methods.
AI-generated from the title and abstract; the full text is not read.
Abstract
In derivative free optimization (DFO), the cosine measure is a value that often arises in the convergence analysis of direct search methods. Given the increasing interest in high-dimensional DFO problems, it is valuable to compute the cosine measure in this setting; however, this has recently been shown to be NP-hard. We propose a new formulation and heuristics to tackle the cosine measure problem in high dimensions. We establish new results that enable the construction of sets with prescribed cosine measures, providing a systematic way to generate test instances for comparing algorithms that compute the cosine measure. Finally, we compare the algorithms proposed in this paper with some existing algorithms from the literature.
The authors' abstract, as published at the source. EURO Journal on Computational Optimization, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics