About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set

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.