Journal of Convex Analysis 24 (2017), No. 2, 493--500
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
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