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New Approach to Solving a System of Variational Inequalities and Hierarchical Problems

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Abstract

This paper deals with a viscosity iterative method, in real Hilbert spaces, for solving a system of variational inequalities over the fixed-point sets of possibly discontinuous mappings. Under classical conditions, we prove a strong convergence theorem for our method. The proposed algorithm can be applied for instance to solving variational inequalities in some situations when the projection methods fail. Moreover, the techniques of analysis are novel and provide new tools in designing approximation schemes for combined and bilevel optimization problems.

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Authors and Affiliations

  1. GRIMAAG, Département Scientifique Interfacultaire, Université des Antilles-Guyane, Campus de Schoelcher, 97233, Martinique, France

    P. E. Maingé

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  1. P. E. Maingé
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Correspondence to P. E. Maingé.

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Communicated by Masao Fukushima.

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Maingé, P.E. New Approach to Solving a System of Variational Inequalities and Hierarchical Problems. J Optim Theory Appl 138, 459–477 (2008). https://doi.org/10.1007/s10957-008-9433-z

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