EKELAND'S VARIATIONAL PRINCIPLE FOR SET-VALUED MAP SWITH APPLICATIONS TO VECTOR OPTIMIZATION IN UNIFORM SPACES

In this paper, we introduce the concept of a weakq-distance and for this distance we derive a set-valued version of Ekeland's variational principle in the setting of uniform spaces. By using this principle, we prove the existence of solutions to a vector optimization problem with a set-valued m...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2014-12, Vol.18 (6), p.1999-2020
Main Authors: Ansari, Qamrul Hasan, Eshghinezhad, Somayeh, Fakhar, Majid
Format: Article
Language:English
Subjects:
Mathematical functions
Mathematical vectors
Online Access:Get full text
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Summary:In this paper, we introduce the concept of a weakq-distance and for this distance we derive a set-valued version of Ekeland's variational principle in the setting of uniform spaces. By using this principle, we prove the existence of solutions to a vector optimization problem with a set-valued map. Moreover, we define the (p, ε)-condition of Takahashi and the (p, ε)-condition of Hamel for a set-valued map. It is shown that these two conditions are equivalent. As an application, we discuss the relationship between anε-approximate solution and a solution of a vector optimization problem with a set-valued map. Also, a well-posedness result for a vector optimization problem with a set-valued map is given. 2010Mathematics Subject Classification: 90C33, 49J40. Key words and phrases: Weakq-distance, Ekeland's variational principle, Vector optimization, Well-posedness.
ISSN:1027-5487
2224-6851