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Existence theorems for multivalued variational inequality problems on uniformly prox-regular sets

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Abstract

In this paper, a multivalued variational inequality problem on uniformly prox-regular set is studied. The existence theorems for such aforementioned problem are presented and, consequently, some algorithms for finding those solutions are also constructed. The results in this paper can be viewed as an improvement of the significant result that presented in Bounkhel et al. (J Inequal Pure Appl Math 4(1), 2003, Article 14).

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Acknowledgments

The authors wish to express their gratitude to the referees for a careful reading of the manuscript and helpful suggestions, especially the Remark 4.5.

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Authors and Affiliations

  1. Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

    Muhammad Aslam Noor

  2. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Narin Petrot & Jittiporn Suwannawit

  3. Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok, 10400, Thailand

    Narin Petrot & Jittiporn Suwannawit

Authors
  1. Muhammad Aslam Noor
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  2. Narin Petrot
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  3. Jittiporn Suwannawit
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Corresponding author

Correspondence to Narin Petrot.

Additional information

This work is supported by the Centre of Excellence in Mathematics, the commission on Higher Education, Thailand.

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Noor, M.A., Petrot, N. & Suwannawit, J. Existence theorems for multivalued variational inequality problems on uniformly prox-regular sets. Optim Lett 8, 99–111 (2014). https://doi.org/10.1007/s11590-012-0545-x

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