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:10.1155/2011/794203Published: 13 March 2011
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 .