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Zbl 1221.49012
Marino, Giuseppe; Xu, Hong-Kun
Explicit hierarchical fixed point approach to variational inequalities. (English)
[J] J. Optim. Theory Appl. 149, No. 1, 61-78 (2011). ISSN 0022-3239; ISSN 1573-2878/e

Summary: An explicit hierarchical fixed point algorithm is introduced to solve monotone variational inequalities, which are governed by a pair of nonexpansive mappings, one of which is used to define the governing operator and the other to define the feasible set. These kinds of variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings. Strong convergence of the algorithm is proved under different circumstances of parameter selections. Applications in hierarchical minimization problems are also included.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
90C33 Complementarity problems

Keywords: variational inequality; nonexpansive mapping; iterative algorithm; hierarchical fixed point; hierarchical minimization; projection

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Zentralblatt MATH Berlin [Germany]