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On Maingé’s Approach for Hierarchical Optimization Problems

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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.

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Acknowledgements

The authors thank Professor Alexander S. Strekolovsky and the referee for their comments and suggestions that improve the presentation of this paper. The first author is thankful to the Development and Promotion of Science and Technology Talents Project (DPST) for financial support. The second author is supported by the Thailand Research Fund, the office of Commission on Higher Education, and Khon Kaen University under grant RMU5380039.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

    Rapeepan Kraikaew & Satit Saejung

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  1. Rapeepan Kraikaew
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  2. Satit Saejung
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Correspondence to Satit Saejung.

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Communicated by Alexander S. Strekolovsky.

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Kraikaew, R., Saejung, S. On Maingé’s Approach for Hierarchical Optimization Problems. J Optim Theory Appl 154, 71–87 (2012). https://doi.org/10.1007/s10957-011-9982-4

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