On Maingé’s Approach for Hierarchical Optimization Problems

Rapeepan Kraikaew () and Satit Saejung ()
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Rapeepan Kraikaew: Khon Kaen University
Satit Saejung: Khon Kaen University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 5, 87 pages

Abstract: Abstract This paper aims at investigating an iterative method for solving a system of variational inequalities with fixed-point set constraints. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé. Strong convergence results are established in the setting of Hilbert spaces. We propose an alternative analysis that allows us to relax some assumption imposed in his paper for convergence of the considered method. As a complementary result, we show how to adapt these processes to the case when the constraints involve operators belonging to the class of hemi-contractive mappings; this goes beyond the scope of Maingé’s result.

Keywords: Fixed points; Hierarchical optimization problems; Nonexpansive mappings (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9982-4

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