A porosity result in convex minimization. (25th May 2005)

• Record Type: Journal Article
• Authors: Howlett, P. G.; Zaslavski, A. J.
• Is Part Of: Abstract and applied analysis. Volume 2005:Number 3(2005)
• Page Start: 319
• Page End: 326
• Publication Date: 2005-05-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/AAA.2005.319
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study the minimization problemf ( x ) → min, x ∈ C, wheref belongs to a complete metric spaceℳ of convex functions and the setC is a countable intersection of a decreasing sequence of closed convex setsC i in a reflexive Banach space. Letℱ be the set of allf ∈ ℳ for which the solutions of the minimization problem over the setC i converge strongly asi → ∞ to the solution over the setC . In our recent work we show that the setℱ contains an everywhere denseG δ subset ofℳ . In this paper, we show that the complementℳ \ ℱ is not only of the first Baire category but also aσ -porous set.