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On the Stability of the Motzkin Representation of Closed Convex Sets

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Abstract

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple \(\left( C,D\right) \) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

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Correspondence to M. I. Todorov.

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M. I. Todorov is on leave from IMI-BAS, Sofia, Bulgaria.

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Goberna, M.A., Todorov, M.I. On the Stability of the Motzkin Representation of Closed Convex Sets. Set-Valued Var. Anal 21, 635–647 (2013). https://doi.org/10.1007/s11228-013-0251-6

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  • DOI: https://doi.org/10.1007/s11228-013-0251-6

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