Research Article
Algorithms Construction for Variational Inequalities
1 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2 Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3 Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
Fixed Point Theory and Applications 2011, 2011:794203 doi:10.1155/2011/794203
Published: 13 March 2011Abstract
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 
.
