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On a Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods

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  • Q. Z. Yang

    (Nankai University)

Abstract

Verma introduced a system of nonlinear variational inequalities and proposed projection methods to solve it. This system reduces to a variational inequality problem under certain conditions. So, at least in form, it can be regarded as a extension of a variational inequality problem. In this note, we show that solving this system coincides exactly with solving a variational inequality problem. Therefore, we conclude that it suffices to study the corresponding variational inequalities.

Suggested Citation

  • Q. Z. Yang, 2006. "On a Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 547-549, September.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:3:d:10.1007_s10957-006-9117-5
    DOI: 10.1007/s10957-006-9117-5
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    References listed on IDEAS

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    1. R. U. Verma, 2004. "Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 203-210, April.
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