A porosity result in convex minimization
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2005
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Howlett, P.G.
Zaslavski, A.
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Abstract and Applied Analysis, 2005; 2005(3):319-326
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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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Copyright 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/3.0/)