Abstract

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.