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Zbl 1216.90092
Iiduka, Hideaki
Iterative algorithm for solving triple-hierarchical constrained optimization problem. (English)
[J] J. Optim. Theory Appl. 148, No. 3, 580-592 (2011). ISSN 0022-3239; ISSN 1573-2878/e

Summary: Many practical problems such as signal processing and network resource allocation are formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms to solve these problems have been proposed. This paper discusses a monotone variational inequality with variational inequality constraint over the fixed point set of a nonexpansive mapping, which is called the triple-hierarchical constrained optimization problem, and presents an iterative algorithm for solving it. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.

MSC 2000:: *90C33 Complementarity problems

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

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