Data loci in algebraic optimization

DOI10.1016/j.jpaa.2022.107144OpenAlexW3041792862MaRDI QIDQ2154277

Jose Israel Rodriguez, Emil Horobeţ

Publication date: 19 July 2022

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.04688

zbMATH Keywords

parametric optimizationdual varietyconstrained critical pointsmaximum likelihood degreeEuclidean distance degreeconormal variety

Mathematics Subject Classification ID

Determinantal varieties (14M12) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Computational aspects in algebraic geometry (14Q99) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• Macaulay2

Cites Work

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• The maximum likelihood data singular locus
• Best rank one approximation of real symmetric tensors can be chosen symmetric
• Degrees of Kalman varieties of tensors
• Solving parametric polynomial systems
• An Introduction to Polynomial and Semi-Algebraic Optimization
• Chapter 5: Dualities
• The data singular and the data isotropic loci for affine cones
• Matrices with eigenvectors in a given subspace
• Euclidean Distance Degree of the Multiview Variety
• Exact Solutions in Structured Low-Rank Approximation
• Counting Critical Formations on a Line
• The Euclidean distance degree of an algebraic variety

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