ICCSA 2005: Computational Science and Its Applications – ICCSA 2005 pp 1341-1348 | Cite as
Some Results on a Class of Optimization Spaces
Abstract
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?
AMS Subject Classification: Primary: 90C48, 90C05; Secondary: 47N10.
Keywords
Interval Linear Programs Partially Ordered Banach spaces Ben-Israel-Charnes SpacesPreview
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