Does continuity of convex-valued maps survive under intersection? (Q2776684)
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scientific article; zbMATH DE number 1714786
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Does continuity of convex-valued maps survive under intersection? |
scientific article; zbMATH DE number 1714786 |
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2001
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set-valued mapping
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Hausdorff metric
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Demyanov metric
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D-regular sets
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convex programming
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0.7983946
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0.7827877
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Does continuity of convex-valued maps survive under intersection? (English)
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The author studies properties of unary and binary operations on compact convex sets with respect to the Demyanov metric (D-metric). He defines a class of D-regular parametric convex-valued maps in terms of the D-metric and notices that this class of variable convex sets is invariant under the arithmetic addition, linear transformation and intersection operation (if the intersection is nonempty). It is shown that the property of D-regularity is conserved under the Argmin operation for standard continuous parametric convex programs.NEWLINENEWLINEFor the entire collection see [Zbl 0974.00048].
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