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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |