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- Title
Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set.
- Authors
Balashov, M. V.
- 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.
- Subjects
METRIC projections; CONVEX sets; LINEAR control systems; ALGORITHMS; NONSMOOTH optimization
- Publication
Mathematical Notes, 2023, Vol 113, Issue 5/6, p632
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434623050036