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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 3, Pages 392–403 (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

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.

DOI: https://doi.org/10.7868/S0044466914030107

Full text: PDF file (273 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:3, 407–417

Bibliographic databases:

Document Type: Article
UDC: 519.626
Received: 24.09.2013

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

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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