Algorithms Construction for Variational Inequalities
Yonghong Yao, Yeong‐Cheng Liou, Shin Min Kang · Fixed Point Theory and Applications · 2011
Abstract We devote this paper to solving the variational inequality of finding "Equation missing" with property "Equation missing" such that "Equation missing" for all "Equation missing". Note that this hierarchical problem is associated with some convex programming problems. For solving the above VI, we suggest two algorithms: Implicit Algorithmml: "Equation missing" for all "Equation missing" and Explicit Algorithm: "Equation missing" for all "Equation missing". 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 "Equation missing".