Abstract
This article is a continuation of Löhne A, Tammer C (2007: A new approach to duality in vector optimization. Optimization 56(1–2):221–239) [14]. We developed in [14] a duality theory for convex vector optimization problems, which is different from other approaches in the literature. The main idea is to embed the image space Rq of the objective function into an appropriate complete lattice, which is a subset of the power set of Rq. This leads to a duality theory which is very analogous to that of scalar convex problems. We applied these results to linear problems and showed duality assertions. However, in [14] we could not answer the question, whether the supremum of the dual linear program is attained in vertices of the dual feasible set. We show in this paper that this is, in general, not true but, it is true under additional assumptions.
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Heyde, F., Löhne, A., Tammer, C. (2009). The Attainment of the Solution of the Dual Program in Vertices for Vectorial Linear Programs. In: Barichard, V., Ehrgott, M., Gandibleux, X., T'Kindt, V. (eds) Multiobjective Programming and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85646-7_2
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