Some results on a class of optimization spaces

Let X be a partially ordered real Banach space, a, b ∈ X with a ≤ b. Let φ be a bounded linear functional on X. We call X a Ben-Israel-Charnes space (or a B-C space, for short) if the linear program: Maximize 〈φ, x〉 subject to a ≤ x ≤ b has an optimal solution. Such problems have been shown to be important in solving a class of problems known as Interval Linear Programs. B-C spaces were introduced by the first author in his doctoral dissertation. In this paper we identify new classes of Banach spaces that are B-C spaces. We also present sufficient conditions under which answers are in the affirmative for the following questions: 1 When is a closed subspace of a B-C space, a, B-C space? 2 Is the range of a bounded linear map from a Banach space into a B-C space, a B-C space? © Springer-Verlag Berlin Heidelberg 2005.