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Minimum and maximum principle sufficiency properties for nonsmooth variational inequalities

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Abstract

This paper deals with the study of minimum and maximum principle sufficiency properties for nonsmooth variational inequalities (in short, NVI) by using gap functions. Several characterizations of these two sufficiency properties are provided. We also discuss the error bound for nonsmooth variational inequalities. Two open questions are given at the end.

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Notes

  1. Remark 1 is due to the Referee.

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Acknowledgments

This research was funded by the National Plan for Science, Technology and Innovation (MAARIFAH)—King Abdulaziz City for Science and Technology—through the Science & Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM)—the Kingdom of Saudi Arabia, award number 12-MAT3023-24. Authors are grateful to the King Fahd University of Petroleum and Minerals, Dhahran Saudi Arabia for providing excellent research facilities to carry out this research. Authors are grateful to the referee for his/her remarks and comments to improve the previous draft of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    M. Alshahrani, S. Al-Homidan & Q. H. Ansari

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Q. H. Ansari

Authors
  1. M. Alshahrani
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  2. S. Al-Homidan
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  3. Q. H. Ansari
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Correspondence to Q. H. Ansari.

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Alshahrani, M., Al-Homidan, S. & Ansari, Q.H. Minimum and maximum principle sufficiency properties for nonsmooth variational inequalities. Optim Lett 10, 805–819 (2016). https://doi.org/10.1007/s11590-015-0906-3

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  • DOI: https://doi.org/10.1007/s11590-015-0906-3

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