Geodesic
Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set
Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 655-666

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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. 
@article{MZM_2023_113_5_a2,
     author = {M. V. Balashov},
     title = {Sufficient {Conditions} for the {Linear} {Convergence} of an {Algorithm} for {Finding} the {Metric} {Projection} of a {Point} onto a {Convex} {Compact} {Set}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {655--666},
     publisher = {mathdoc},
     volume = {113},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a2/}
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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. Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 655-666. http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a2/