Open Access

Algorithms Construction for Variational Inequalities

Fixed Point Theory and Applications20112011:794203

https://doi.org/10.1155/2011/794203

Received: 4 October 2010

Accepted: 19 February 2011

Published: 13 March 2011

Abstract

We devote this paper to solving the variational inequality of finding with property such that for all . Note that this hierarchical problem is associated with some convex programming problems. For solving the above VI, we suggest two algorithms: Implicit Algorithmml: for all and Explicit Algorithm: for all . It is shown that these two algorithms converge strongly to the unique solution of the above VI. As special cases, we prove that the proposed algorithms strongly converge to the minimum norm fixed point of .

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Mathematics, Tianjin Polytechnic University
(2)
Department of Information Management, Cheng Shiu University
(3)
Department of Mathematics and RINS, Gyeongsang National University

Copyright

© Yonghong Yao et al. 2011

This article is published under license to BioMed Central Ltd. 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.