A porosity result in convex minimization

P. G. Howlett and A. J. Zaslavski

Abstract and Applied Analysis, 2005, vol. 2005, 1-8

Abstract:

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 C i 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 C i 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 G δ 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:908454

DOI: 10.1155/AAA.2005.319

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