Saddle points and gap functions for vector equilibrium problems via conjugate duality in vector optimization

In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functi...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-07, Vol.343 (2), p.853-865
Main Authors: Li, S.J., Yao, S.F., Chen, C.R.
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Conjugate duality
Exact sciences and technology
Gap function
Inclusion relations
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Saddle point
Sciences and techniques of general use
Vector optimization
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Summary:In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functions for a vector equilibrium problem are established by using the weak and strong duality.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.02.009