Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29839
Title: Further study on the Levitin-Polyak well-posedness of constrained convex vector optimization problems
Authors: Huang, XX
Yang, XQ 
Keywords: Convex vector optimization
Cone-constrained optimization
Weakly efficient solution set
Well-posedness
Ekeland's variational principle
Issue Date: 2012
Publisher: Pergamon Press
Source: Nonlinear analysis : theory, methods and applications, 2012, v. 75, no. 3, p. 1341-1347 How to cite?
Journal: Nonlinear analysis : theory, methods and applications 
Abstract: In this paper, we first establish characterizations of the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with a general ordering cone (with or without a cone constraint) defined in a finite dimensional space. Using one of the characterizations, we further establish for a convex vector optimization problem with a general ordering cone and a cone constraint defined in a finite dimensional space the equivalence between the nonemptiness and compactness of its weakly efficient solution set and the generalized type I Levitin-Polyak well-posednesses. Finally, for a cone-constrained convex vector optimization problem defined in a Banach space, we derive sufficient conditions for guaranteeing the generalized type I Levitin-Polyak well-posedness of the problem.
URI: http://hdl.handle.net/10397/29839
ISSN: 0362-546X
DOI: 10.1016/j.na.2011.01.012
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