Linear Optimization with Box Constraints in Banach Spaces.

Let X be a partially ordered real Banach space, let a, b∈ X with a≤ b. Let φ be a bounded linear functional on X. We say that X satisfies the box-optimization property (or X is a BOP space) if the box-constrained linear program: max 〈 φ, x〉, s.t. a≤ x≤ b, has an optimal solution for any φ, a and b. Such problems arise naturally in solving a class of problems known as interval linear programs. BOP spaces were introduced (in a different language) and systematically studied in the first author’s doctoral thesis. In this paper, we identify new classes of Banach spaces that are BOP spaces. We present also sufficient conditions under which answers are in the affirmative for the following questions: [ABSTRACT FROM AUTHOR]