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Strict vector variational inequalities and strict Pareto efficiency in nonconvex vector optimization

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Abstract

In this paper, we consider a vector optimization problem involving the difference of two cone convex functions in Banach spaces. In terms of Clarke subdifferential, we formulate strict Minty vector variational inequality problem and strict Stampacchia vector variational inequality problem. We mainly study the relationships between the solutions of these vector variational inequality problems and the strict Pareto efficient solution of the vector optimization problem.

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Acknowledgments

The author expresses his deep gratitude to the referees for helpful comments which improve this paper. The research was supported by IRTSTYN and the National Natural Science Foundation of China under Grant No. 11371312 and 11261067.

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  1. Department of Mathematics, Yunnan University, Kunming, 650091, People’s Republic of China

    Hui Huang

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  1. Hui Huang
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Huang, H. Strict vector variational inequalities and strict Pareto efficiency in nonconvex vector optimization. Positivity 19, 95–109 (2015). https://doi.org/10.1007/s11117-014-0285-5

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