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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 3, Pages 392–403
DOI: https://doi.org/10.7868/S0044466914030107 (Mi zvmmf10001) 		 
On the sensitivity of a Euclidean projection

A. F. Izmailov, A. S. Kurennoy

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
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DOI: https://doi.org/10.7868/S0044466914030107
Abstract: The structure and behavior of Euclidean projections of a point onto a set defined by parametric constraints is studied. Under the Mangasarian–Fromovitz constraint qualification, it is shown that the projection is locally unique and continuous and, if the feasible set is constant, locally Lipschitz continuous as well. Quantitative results are obtained characterizing the asymptotic behavior of projections under perturbations in a given direction.
Key words: Euclidean projection, sensitivity, strong regularity, strong stability, Mangasarian–Fromovitz constraint qualification, linear independence constraint qualification, constant rank constraint qualification, directional regularity.
Received: 24.09.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 3, Pages 407–417
DOI: https://doi.org/10.1134/S0965542514030099
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: A. F. Izmailov, A. S. Kurennoy, “On the sensitivity of a Euclidean projection”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 392–403; Comput. Math. Math. Phys., 54:3 (2014), 407–417
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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