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On Maingé’s Approach for Hierarchical Optimization Problems

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  • Rapeepan Kraikaew

    (Khon Kaen University)

  • Satit Saejung

    (Khon Kaen University)

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.

Suggested Citation

  • Rapeepan Kraikaew & Satit Saejung, 2012. "On Maingé’s Approach for Hierarchical Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 71-87, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-011-9982-4
    DOI: 10.1007/s10957-011-9982-4
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    References listed on IDEAS

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    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    3. Kassay, Gabor & Kolumban, Jozsef & Pales, Zsolt, 2002. "Factorization of Minty and Stampacchia variational inequality systems," European Journal of Operational Research, Elsevier, vol. 143(2), pages 377-389, December.
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