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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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 |
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doaj-3b76be5761fa482392edf7e2557ba17e2020-11-24T22:40:13ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092005-01-012005328730510.1155/AAA.2005.287σ-porosity in monotonic analysis with applications to optimizationA. M. Rubinov0School of Information Technology and Mathematical Sciences (SITMS), Centre for Informatics and Applied Optimization, University of Ballarat, Ballarat Victoria 3353, AustraliaWe 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.http://dx.doi.org/10.1155/AAA.2005.287 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. M. Rubinov |
| spellingShingle |
A. M. Rubinov σ-porosity in monotonic analysis with applications to optimization Abstract and Applied Analysis |
| author_facet |
A. M. Rubinov |
| author_sort |
A. M. Rubinov |
| title |
σ-porosity in monotonic analysis with applications to optimization |
| title_short |
σ-porosity in monotonic analysis with applications to optimization |
| title_full |
σ-porosity in monotonic analysis with applications to optimization |
| title_fullStr |
σ-porosity in monotonic analysis with applications to optimization |
| title_full_unstemmed |
σ-porosity in monotonic analysis with applications to optimization |
| title_sort |
σ-porosity in monotonic analysis with applications to optimization |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2005-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/AAA.2005.287 |
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AT amrubinov sporosityinmonotonicanalysiswithapplicationstooptimization |
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