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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

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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