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Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set

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Abstract

Many problems, for example, problems on the properties of the reachability 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 with a linear rate. An example is used to illustrate the importance of such conditions.

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Funding

This work was supported by the Russian Science Foundation under grant no. 22-11-00042, https://rscf.ru/en/project/22-11-00042/, at Institute of Control Sciences.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, 117997, Russia

    M. V. Balashov

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  1. M. V. Balashov
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Correspondence to M. V. Balashov.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 655–666 https://doi.org/10.4213/mzm13745.

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Balashov, M.V. Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set. Math Notes 113, 632–641 (2023). https://doi.org/10.1134/S0001434623050036

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  • DOI: https://doi.org/10.1134/S0001434623050036

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