Abstract
We study translation invariant functionals where the involved set is constructed by block norms or oblique norms. These sets are described by linear inequalities. We characterize efficient elements by means of functionals where oblique norms are involved and weakly efficient elements via scalarization using block norms. Our results are applied to multiobjective d.c. (difference of convex functions) optimization problems. Furthermore, we discuss several fundamental properties of the directional minimal time function that are important for applications in locational analysis. We present relationships between the nonlinear translation invariant functionals and the oriented distance by Hiriart-Urruty.
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Tammer, C., Weidner, P. (2020). Special Cases and Functionals Related to \(\varphi _{A,k}\). In: Scalarization and Separation by Translation Invariant Functions. Vector Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-44723-6_9
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DOI: https://doi.org/10.1007/978-3-030-44723-6_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44721-2
Online ISBN: 978-3-030-44723-6
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