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Zbl 1238.65061
Iiduka, Hideaki
Strong convergence for an iterative method for the triple-hierarchical constrained optimization problem. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e1292-e1297 (2009). ISSN 0362-546X

Summary: The variational inequality problem for a monotone operator over the fixed point set of a nonexpansive mapping is connected with many signal processing problems, and such problems have hierarchical structure, for example, the convex optimization problem over the solution set of the variational inequality problem over the fixed point set has triple-hierarchical structure. In this paper, we present an iterative algorithm for this problem. The strong convergence for the proposed algorithm to the solution is guaranteed under some assumptions.

MSC 2000:: *65K15
47N10 Appl. of operator theory in optimization, math. programming, etc.
49J40 Variational methods including variational inequalities
47J25 Methods for solving nonlinear operator equations (general)
90C33 Complementarity problems

Keywords: hierarchical constrained optimization problem; variational inequality problem; monotone operator; nonexpansive mapping; fixed point; strong convergence

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