Explicit Hierarchical Fixed Point Approach to Variational Inequalities

Giuseppe Marino () and Hong-Kun Xu ()
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Giuseppe Marino: Universita della Calabria
Hong-Kun Xu: National Sun Yat-sen University

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 1, No 4, 78 pages

Abstract: Abstract 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.

Keywords: Variational inequality; Nonexpansive mapping; Iterative algorithm; Hierarchical fixed point; Hierarchical minimization; Projection (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-010-9775-1

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