Geodesic
The gradient projection algorithm for a~proximally smooth set and a~function with Lipschitz continuous gradient
Sbornik. Mathematics, Tome 211 (2020) no. 4, pp. 481-504

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We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound condition with exponent $\alpha\in(0,1]$ for the gradient mapping. Under this condition, it is shown that the standard gradient projection algorithm converges to a solution of the problem linearly or sublinearly, depending on the value of the exponent $\alpha$. This paper is theoretical. Bibliography: 23 titles.
Keywords: gradient mapping, error bound condition, proximal smoothness, nonconvex extremal problem.
Mots-clés : gradient projection algorithm 
@article{SM_2020_211_4_a0,
     author = {M. V. Balashov},
     title = {The gradient projection algorithm for a~proximally smooth set and a~function with {Lipschitz} continuous gradient},
     journal = {Sbornik. Mathematics},
     pages = {481--504},
     publisher = {mathdoc},
     volume = {211},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_4_a0/}
}
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M. V. Balashov. The gradient projection algorithm for a~proximally smooth set and a~function with Lipschitz continuous gradient. Sbornik. Mathematics, Tome 211 (2020) no. 4, pp. 481-504. http://geodesic.mathdoc.fr/item/SM_2020_211_4_a0/