Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Maxim V. Balashov

Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny, Moscow region, Russia 141700

balashov73@mail.ru

Keywords

  • Hilbert space
  • strongly convex set of radius r
  • proximally smooth set with constant R
  • Lipschitz continuous gradient
  • gradient projection algorithm
  • continuous optimization

Mathematics Subject Classification

46C05, 52A07, 49J52; 46N10, 90C26, 26B25

Suggested citation

M. V. Balashov. “About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set.” Journal of Convex Analysis 24 (2017), No. 2, 493–500. https://doi.org/10.68381/jca24031

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2017. Rights now held by Banach Press.