The gradient projection algorithm for a proximally smooth set and a function with Lipschitz continuous gradient
Maxim Viktorovich Balashov · Sbornik Mathematics · 2019
Abstract We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound condition with exponent for the gradient mapping. Under this condition, it is shown that the standard gradient projection algorithm converges to a solution of the problem linearly or sublinearly, depending on the value of the exponent . This paper is theoretical. Bibliography: 23 titles.