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Generalized Gerstewitz’s Functions and Vector Variational Principle for ε-Efficient Solutions in the Sense of Németh

  • Jing Hui QiuEmail author
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Abstract

In this paper, we first generalize Gerstewitz’s functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904–937 (2014)]. By using the generalized Gerstewitz’s functions and the partial order principle, we obtain a vector EVP for ε-efficient solutions in the sense of Németh, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.

Keywords

Ekeland variational principle partial order principle ε-efficient solutions in the sense of Németh Gerstewitz’s function convex cone 

MR(2010) Subject Classification

46A03 49J53 58E30 65K10 

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Notes

Acknowledgements

The author is grateful to the reviewers for their valuable comments and suggestions.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesSoochow UniversitySuzhouP. R. China

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