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Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency

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Abstract

This paper deals with the relations between vector variational inequality problems and nonsmooth vector optimization problems using the concept of quasi efficiency. We identify the vector critical points, the weak quasi efficient points and the solutions of the weak vector variational inequality problems under generalized approximate convexity assumptions. To the best of our knowledge such results have not been established till now.

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Acknowledgments

The authors are grateful to the anonymous referees for their valuable suggestions that helped to improve the paper in its present form.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    S. K. Mishra & B. B. Upadhyay

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  1. S. K. Mishra
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  2. B. B. Upadhyay
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Correspondence to S. K. Mishra.

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This author is supported by the Council of Scientific and Industrial Research, New Delhi, India, through grant no. 09/013(0357)/2011-EMR-I.

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Mishra, S.K., Upadhyay, B.B. Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency. Positivity 17, 1071–1083 (2013). https://doi.org/10.1007/s11117-013-0221-0

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