A revised pre-order principle and set-valued Ekeland variational principles with generalized distances |
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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 my former paper “A pre-order principle and set-valued Ekeland variational principle” (see J. Math. Anal. Appl., 419, 904–937 (2014)]), we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles (denoted by EVPs) in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy’s EVP in On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381–396 (2011)], where the perturbation contains a weak τ-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy’s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances. |
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Keywords: | Pre-order principle Ekeland variational principle set-valued map perturbation locally convex space vector optimization |
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