Journal of Applied Mathematics
Volume 2012 (2012), Article ID 142862, 13 pages
http://dx.doi.org/10.1155/2012/142862
Research Article

Convergence of a Proximal Point Algorithm for Solving Minimization Problems

Abdelouahed Hamdi,1 M. A. Noor,2 and A. A. Mukheimer1

1Department of Mathematics, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
2Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

Received 16 January 2012; Accepted 4 February 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Abdelouahed Hamdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones.