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This article is cited in 3 scientific papers (total in 3 papers)
Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set
M. V. Balashov V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
Abstract:
Many problems, for example, problems on the properties of the attainability set of a linear control system, are reduced to finding the projection of zero onto some convex compact subset in a finite-dimensional Euclidean space. This set is given by its support function. In this paper, we discuss some minimum sufficient conditions that must be imposed on a convex compact set so that the gradient projection method for solving the problem of finding the projection of zero onto this set converges at a linear rate. An example is used to illustrate the importance of such conditions.
Keywords:
gradient projection method, supporting ball, function growth conditions, nonsmooth analysis.
Received: 26.09.2022 Revised: 16.12.2022
Citation:
M. V. Balashov, “Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set”, Mat. Zametki, 113:5 (2023), 655–666; Math. Notes, 113:5 (2023), 632–641
Linking options:
https://www.mathnet.ru/eng/mzm13745https://doi.org/10.4213/mzm13745 https://www.mathnet.ru/eng/mzm/v113/i5/p655
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Abstract page: | 156 | Full-text PDF : | 5 | Russian version HTML: | 98 | References: | 24 | First page: | 7 |
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