A Porosity Result in Convex Minimization

نویسندگان

  • P. G. HOWLETT
  • A. J. ZASLAVSKI
چکیده

We study the minimization problem f (x) → min, x ∈ C, 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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تاریخ انتشار 2005