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.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11471236 and 11561049)
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Qiu, J.H. Generalized Gerstewitz’s Functions and Vector Variational Principle for ϵ-Efficient Solutions in the Sense of Németh. Acta. Math. Sin.-English Ser. 35, 297–320 (2019). https://doi.org/10.1007/s10114-018-7159-x
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DOI: https://doi.org/10.1007/s10114-018-7159-x
Keywords
- Ekeland variational principle
- partial order principle
- ε-efficient solutions in the sense of Németh
- Gerstewitz’s function
- convex cone