Classical linear vector optimization duality revisited

Details Classical linear vector optimization duality revisited Classical linear vector optimization duality revisited

2010-05-07

arxiv.org/abs/1005.1151v1

Mathematics

Optimization and Control

10 pages

Scientific paper

10.1007/s11590-010-0263-1

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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