Lagrange duality, stability and subdifferentials in vector optimization

Lagrange duality theorems for vector and set optimization problems which are based on a consequent usage of infimum and supremum (in the sense of greatest lower and least upper bounds with respect to a partial ordering) have been recently proven. In this note, we provide an alternative proof of stro...

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Bibliographic Details
Published in:Optimization 2013-03, Vol.62 (3), p.415-428
Main Authors: Hernández, Elvira, Löhne, Andreas, Rodríguez-Marín, Luis, Tammer, Christiane
Format: Article
Language:English
Subjects:
duality
Infimum
Lagrange multiplier
Mathematical analysis
Mathematical problems
Operators
Optimization
Scalars
Stability
Studies
subdifferential
Theorems
Upper bounds
Variables
vector optimization
Vectors (mathematics)
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Summary:Lagrange duality theorems for vector and set optimization problems which are based on a consequent usage of infimum and supremum (in the sense of greatest lower and least upper bounds with respect to a partial ordering) have been recently proven. In this note, we provide an alternative proof of strong duality for such problems via suitable stability and subdifferential notions. In contrast to most of the related results in the literature, the space of dual variables is the same as in the scalar case, i.e. a dual variable is a vector rather than an operator. We point out that duality with operators is an easy consequence of duality with vectors as dual variables.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2013.766187