A partial order principle and vector variational principle for ε-efficient solutions in the sense of Németh

2016/11/10 by Jinghui Qiu, Jing-Hui Qiu, Qiu, Jing-Hui
Computer Science · Mathematics · #49J53 #58E30 #65K10 #90C48 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Optimization and Variational Analysis #math.FA #msc:49J53 #msc:58E30 #msc:65K10 #msc:90C48

paper · pdf · doi:10.48550/arxiv.1611.03301

28 pages

arxiv created 2016/11/10 · openalex publication_date 2016/11/10 · arxiv updated 2016/11/11 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a partial order principle, which is useful to deriving vector Ekeland variational principle (denoted by EVP). By using the partial order principle and extending Gerstewitz's functions, we obtain a vector EVP for ε-efficient solutions in the sense of Németh, which essentially improves the earlier results by removing a usual assumption for boundedness of range 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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