Abstract
We study properties of unary and binary operations on compact convex sets with respect to the Demyanov metric (D-metric). A class of D-regular parametric convex-valued maps is defined in terms of the D-metric. This class of variable convex sets is invariant under the arithmetic addition linear transformation, and also the intersection operation, if, additionally, the intersection is nonempty. The property of D-regularity is shown to be conserved under the Argmin operation for standard continuous parametric convex programs.
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Vladimirov, A. (2001). Does Continuity of Convex-Valued Maps Survive Under Intersection?. In: Rubinov, A., Glover, B. (eds) Optimization and Related Topics. Applied Optimization, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6099-6_20
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DOI: https://doi.org/10.1007/978-1-4757-6099-6_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4844-1
Online ISBN: 978-1-4757-6099-6
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