Algorithms Construction for Variational Inequalities
© Yonghong Yao et al. 2011
Received: 4 October 2010
Accepted: 19 February 2011
Published: 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 .
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