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A porosity result in convex minimization

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  • P. G. Howlett
  • A. J. Zaslavski

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 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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Handle: RePEc:wly:jnlaaa:v:2005:y:2005:i:3:p:319-326
DOI: 10.1155/AAA.2005.319
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