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25 May 2005 A porosity result in convex minimization
P. G. Howlett, A. J. Zaslavski
Abstr. Appl. Anal. 2005(3): 319-326 (25 May 2005). DOI: 10.1155/AAA.2005.319


We study the minimization problem f(x)min, xC, where f belongs to a complete metric space 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 be the set of all f 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 contains an everywhere dense Gδ subset of . In this paper, we show that the complement \ is not only of the first Baire category but also a σ-porous set.


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P. G. Howlett. A. J. Zaslavski. "A porosity result in convex minimization." Abstr. Appl. Anal. 2005 (3) 319 - 326, 25 May 2005.


Published: 25 May 2005
First available in Project Euclid: 25 July 2005

zbMATH: 1091.49019
MathSciNet: MR2197123
Digital Object Identifier: 10.1155/AAA.2005.319

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 3 • 25 May 2005
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