Report
Ekeland variational principles with set-valued objective functions and set-valued perturbations
| العنوان: | Ekeland variational principles with set-valued objective functions and set-valued perturbations |
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| المؤلفون: | Qiu, Jing-Hui |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis |
| الوصف: | In the setting of real vector spaces, we establish a general set-valued Ekeland variational principle (briefly, denoted by EVP), where the objective function is a set-valued map taking values in a real vector space quasi-ordered by a convex cone $K$ and the perturbation consists of a $K$-convex subset $H$ of the ordering cone $K$ multiplied by the distance function. Here, the assumption on lower boundedness of the objective function is taken to be the weakest kind. From the general set-valued EVP, we deduce a number of particular versions of set-valued EVP, which extend and improve the related results in the literature. In particular, we give several EVPs for approximately efficient solutions in set-valued optimization, where a usual assumption for $K$-boundedness (by scalarization) of the objective function's range is removed. Moreover, still under the weakest lower boundedness condition, we present a set-valued EVP, where the objective function is a set-valued map taking values in a quasi-ordered topological vector space and the perturbation consists of a $\sigma$-convex subset of the ordering cone multiplied by the distance function. Comment: 43 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1708.05126 |
| رقم الانضمام: | edsarx.1708.05126 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |