Generalized Gerstewitz's Functions and Vector Variational Principle for-Efficient Solutions in the Sense of Németh |
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基金项目: | Supported by the National Natural Science Foundation of China (Grant Nos. 11471236 and 11561049) |
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摘 要: | 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-efficient solutions in the sense of N′emeth, 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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Generalized Gerstewitz’s Functions and Vector Variational Principle for ϵ-Efficient Solutions in the Sense of Németh |
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Authors: | Jing Hui Qiu |
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Institution: | School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China |
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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. |
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Keywords: | Ekeland variational principle partial order principle ε-efficient solutions in the sense of Németh Gerstewitz's function convex cone |
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