A porosity result in convex minimization. (25th May 2005) - Howlett, P. G.; Zaslavski, A. J.
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.