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) if the linear program defined by Maximize ϕ(x) subject to 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. B-C spaces were introduced in the author's doctoral thesis and were subsequently studied in [8] and [9]. In this article, we review these results, study their implications to certain positive operators over partially ordered Banach spaces and obtain some new ones.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-16,
author = {K. C. Sivakumar},
title = {Applications of nonnegative operators to a class of optimization problems},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {197-202},
zbl = {1145.90104},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-16}
}
K. C. Sivakumar. Applications of nonnegative operators to a class of optimization problems. Banach Center Publications, Tome 83 (2008) pp. 197-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-16/