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Nonsmooth variational-like inequalities and nonsmooth vector optimization

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Abstract

In this paper, we consider nonsmooth vector variational-like inequalities and nonsmooth vector optimization problems. By using the scalarization method, we define nonsmooth variational-like inequalities by means of Clarke generalized directional derivative and study their relations with the vector optimizations and the scalarized optimization problems. Some existence results for solutions of our nonsmooth variational-like inequalities are presented under densely pseudomonotonicity or pseudomonotonicity assumption.

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Acknowledgments

This research was done during the stay of second author at King Fahd University of Petroleum & Minerals, Dhahran Saudi Arabia. It was supported by a KFUPM funded project No. IN 101009.

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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, Q. H. Ansari & S. Al-Homidan

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

    Q. H. Ansari

Authors
  1. M. Alshahrani
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  2. Q. H. Ansari
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  3. S. Al-Homidan
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Corresponding author

Correspondence to Q. H. Ansari.

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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.

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Alshahrani, M., Ansari, Q.H. & Al-Homidan, S. Nonsmooth variational-like inequalities and nonsmooth vector optimization. Optim Lett 8, 739–751 (2014). https://doi.org/10.1007/s11590-013-0614-9

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  • DOI: https://doi.org/10.1007/s11590-013-0614-9

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