Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617249 | Journal of Mathematical Analysis and Applications | 2012 | 7 Pages |
Abstract
We consider the metric projection operator from the real Hilbert space onto a strongly convex set. We prove that the restriction of this operator on the complement of some neighborhood of the strongly convex set is Lipschitz continuous with the Lipschitz constant strictly less than 1. This property characterizes the class of strongly convex sets and (to a certain degree) the Hilbert space. We apply the results obtained to the question concerning the rate of convergence for the gradient projection algorithm with differentiable convex function and strongly convex set.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Maxim V. Balashov, Maxim O. Golubev,