Classical linear vector optimization duality revisited

Classical linear vector optimization duality revisited

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Article ID: iaor2012334
Volume: 6
Issue: 1
Start Page Number: 199
End Page Number: 210
Publication Date: Jan 2012
Journal: Optimization Letters
Authors: , ,
Keywords: duality, vector optimization
Abstract:

With this note we bring again into attention a vector dual problem neglected by the contributions who have recently announced the successful healing of the trouble encountered by the classical duals to the classical linear vector optimization problem. This vector dual problem has, different to the mentioned works which are of set‐valued nature, a vector objective function. Weak, strong and converse duality for this ‘new‐old’ vector dual problem are proven and we also investigate its connections to other vector duals considered in the same framework in the literature. We also show that the efficient solutions of the classical linear vector optimization problem coincide with its properly efficient solutions (in any sense) when the image space is partially ordered by a nontrivial pointed closed convex cone, too.

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