Cited By
View all- Breiding PÇelik TDuff THeaton AMaraj ASattelberger AVenturello LYürük O(2021)Nonlinear Algebra and ApplicationsNumerical Algebra, Control & Optimization10.3934/naco.2021045(0)Online publication date: 2021
Algebraic optimization degree
Authors: 
Marc Härkönen, Benjamin Hollering, Fatemeh Tarashi Kashani, Jose Israel RodriguezAuthors Info & Claims
Pages 44 - 48
Abstract
The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees. Special features include determining Euclidean distance degrees and maximum likelihood degrees. To our knowledge, this is the first comprehensive software package combining different methods in algebraic optimization. The package is available at https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/ISSAC-AlgOpt/alg-stat/AlgebraicOptimization.
References
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C. Améndola, N. Bliss, I. Burke, C. R. Gibbons, M. Helmer, S. Hosten, E. D. Nash, J. I. Rodriguez, and D. Smolkin. The maximum likelihood degree of toric varieties. J. Symbolic Comput., 92:222--242, 2019.
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F. Catanese, S. Hoşten, A. Khetan, and B. Sturmfels. The maximum likelihood degree. Amer. J. Math., 128(3):671--697, 2006.
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J. Draisma, E. Horobeţ, G. Ottaviani, B. Sturmfels, and R. R. Thomas. The Euclidean distance degree of an algebraic variety. Found. Comput. Math., 16(1):99--149, 2016.
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H.-C. Graf von Bothmer and K. Ranestad. A general formula for the algebraic degree in semidefinite programming. Bull. Lond. Math. Soc., 41(2):193--197, 2009.
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D. R. Grayson and M. E. Stillman. Macaulay2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/.
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S. Hoşten, A. Khetan, and B. Sturmfels. Solving the likelihood equations. Found. Comput. Math., 5(4):389--407, 2005.
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P. Rostalski and B. Sturmfels. Dualities. In Semidefinite optimization and convex algebraic geometry, volume 13 of MOS-SIAM Ser. Optim., pages 203--249. SIAM, Philadelphia, PA, 2013.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 29 September 2020
Published in SIGSAM-CCA Volume 54, Issue 2
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Cited By
View all- Breiding PÇelik TDuff THeaton AMaraj ASattelberger AVenturello LYürük O(2021)Nonlinear Algebra and ApplicationsNumerical Algebra, Control & Optimization10.3934/naco.2021045(0)Online publication date: 2021
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