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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 515902, 10 pages
http://dx.doi.org/10.1155/2013/515902
Research Article

The Strong Convergence of Prediction-Correction and Relaxed Hybrid Steepest-Descent Method for Variational Inequalities

1School of Computer Science, Civil Aviation Flight University of China, Guanghan 618307, China
2School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 22 June 2013; Accepted 19 August 2013

Academic Editor: Xu Minghua

Copyright © 2013 Haiwen Xu. 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 establish the strong convergence of prediction-correction and relaxed hybrid steepest-descent method (PRH method) for variational inequalities under some suitable conditions that simplify the proof. And it is to be noted that the proof is different from the previous results and also is not similar to the previous results. More importantly, we design a set of practical numerical experiments. The results demonstrate that the PRH method under some descent directions is more slightly efficient than that of the modified and relaxed hybrid steepest-descent method, and the PRH Method under some new conditions is more efficient than that under some old conditions.