The theory of Vector Optimization is developed by a systematic
usage of infimum and supremum. In order to get existence and
appropriate properties of the infimum, the image space of the
vector optimization problem is embedded into a larger space, which
is a subset of the power set, in fact, the space of self-infimal
sets. Based on this idea we establish solution concepts, existence
and duality results and algorithms for the linear case. The main
advantage of this approach is the high degree of analogy to
corresponding results of Scalar Optimization. The concepts and
results are used to explain and to improve practically relevant
algorithms for linear vector optimization problems.
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