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Algorithms Construction for Variational Inequalities
Fixed Point Theory and Applications volume 2011, Article number: 794203 (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 
.
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Yao, Y., Liou, YC. & Kang, S.M. Algorithms Construction for Variational Inequalities. Fixed Point Theory Appl 2011, 794203 (2011). https://doi.org/10.1155/2011/794203
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DOI: https://doi.org/10.1155/2011/794203