σ-porosity in monotonic analysis with applications to optimization
We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of str...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.287 |
| Summary: | We introduce and study some metric spaces of increasing positively
homogeneous (IPH) functions, decreasing functions, and conormal
(upward) sets. We prove that the complements of the subset of
strictly increasing IPH functions, of the subset of strictly
decreasing functions, and of the subset of strictly conormal sets
are σ-porous in corresponding spaces. Some applications to
optimization are given. |
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| ISSN: | 1085-3375 1687-0409 |