A revised pre-order principle and set-valued Ekeland variational principles with generalized distances

作者：Qiu, Jing Hui^*

来源：Acta Mathematica Sinica-English Series, 2017, 33(6): 775-792.

DOI：10.1007/s10114-017-5062-5

• Pre-order principle
• Ekeland variational principle
• set-valued map
• perturbation
• locally convex space
• vector optimization

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 tau-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.

• 出版日期2017-6
• 单位苏州大学