A porosity result in convex minimization
We study the minimization problem f(x)→min, x∈C, where f belongs to a complete metric space ℳ of convex functions and the set C is a countable intersection of a decreasing sequence of closed convex sets Ci in a reflexive Banach space. Let ℱ be the set of all f∈ℳ for which the solutions of the mini...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.319 |
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| author | P. G. Howlett A. J. Zaslavski |
| author_facet | P. G. Howlett A. J. Zaslavski |
| author_sort | P. G. Howlett |
| collection | DOAJ |
| description | We study the minimization problem f(x)→min, x∈C,
where f belongs to a complete metric space ℳ of
convex functions and the set C is a countable intersection of a
decreasing sequence of closed convex sets Ci in a reflexive
Banach space. Let ℱ
be the set of all f∈ℳ
for which the solutions of the minimization problem
over the set Ci converge strongly as i→∞ to the solution over the set C. In our recent work we show that
the set ℱ contains an everywhere dense Gδ subset of ℳ. In this paper, we show that the
complement ℳ\ℱ is not only of the
first Baire category but also a σ-porous set. |
| format | Article |
| id | doaj-art-91a57ca547524f2d9a39ae279afa21fd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-91a57ca547524f2d9a39ae279afa21fd2025-02-03T01:21:17ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005331932610.1155/AAA.2005.319A porosity result in convex minimizationP. G. Howlett0A. J. Zaslavski1Centre for Industrial and Applied Mathematics (CIAM), University of South Australia, Mawson Lakes, 5059, SA, AustraliaDepartment of Mathematics, Mathematics, Technion – Israel Technology Institute, Haifa 32000, IsraelWe study the minimization problem f(x)→min, x∈C, where f belongs to a complete metric space ℳ of convex functions and the set C is a countable intersection of a decreasing sequence of closed convex sets Ci in a reflexive Banach space. Let ℱ be the set of all f∈ℳ for which the solutions of the minimization problem over the set Ci converge strongly as i→∞ to the solution over the set C. In our recent work we show that the set ℱ contains an everywhere dense Gδ subset of ℳ. In this paper, we show that the complement ℳ\ℱ is not only of the first Baire category but also a σ-porous set.http://dx.doi.org/10.1155/AAA.2005.319 |
| spellingShingle | P. G. Howlett A. J. Zaslavski A porosity result in convex minimization Abstract and Applied Analysis |
| title | A porosity result in convex minimization |
| title_full | A porosity result in convex minimization |
| title_fullStr | A porosity result in convex minimization |
| title_full_unstemmed | A porosity result in convex minimization |
| title_short | A porosity result in convex minimization |
| title_sort | porosity result in convex minimization |
| url | http://dx.doi.org/10.1155/AAA.2005.319 |
| work_keys_str_mv | AT pghowlett aporosityresultinconvexminimization AT ajzaslavski aporosityresultinconvexminimization AT pghowlett porosityresultinconvexminimization AT ajzaslavski porosityresultinconvexminimization |