
Journal of Convex Analysis 24 (2017), No. 2, 493500 Copyright Heldermann Verlag 2017 About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set Maxim V. Balashov Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny, Moscow region, Russia 141700 balashov73@mail.ru We consider the gradient projection algorithm for a strongly convex function with the Lipschitz continuous gradient and a proximally smooth (nonconvex in general) set in a real Hilbert space. We prove that the problem of minimization of such function on a proximally smooth set has unique solution if the constant of proximal smoothness of the set is sufficiently large. The considered algorithm converges with the rate of geometric progression. Keywords: Hilbert space, strongly convex set of radius r, proximally smooth set with constant R, Lipschitz continuous gradient, gradient projection algorithm, continuous optimization. MSC: 46C05, 52A07, 49J52; 46N10, 90C26, 26B25 [ Fulltextpdf (106 KB)] for subscribers only. 