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Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization. (English) Zbl 1272.49022

Summary: Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as a monotone variational inequality over the fixed-point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed-point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proved. Applications of these results to the constrained generalized pseudoinverse are included.

MSC:

49J40 Variational inequalities
65K05 Numerical mathematical programming methods
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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