On the Stability of the Motzkin Representation of Closed Convex Sets |
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| Authors: | M A Goberna M I Todorov |
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| Institution: | 1. Department of Statistics and Operations Research, Universidad de Alicante, Alicante, Spain
2. Department Actuary and Mathematics, Universidad de las Américas, Cholula, Puebla, Mexico
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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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