Applications of nonnegative operators to a class of optimization problems

K. C. Sivakumar. "Applications of nonnegative operators to a class of optimization problems." Banach Center Publications 79.1 (2008): 197-202. <http://eudml.org/doc/286205>.

@article{K2008,
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) 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.},
author = {K. C. Sivakumar},
journal = {Banach Center Publications},
keywords = {partially ordered Banach spaces; Ben-Israel–Charnes spaces},
language = {eng},
number = {1},
pages = {197-202},
title = {Applications of nonnegative operators to a class of optimization problems},
url = {http://eudml.org/doc/286205},
volume = {79},
year = {2008},
}

TY - JOUR
AU - K. C. Sivakumar
TI - Applications of nonnegative operators to a class of optimization problems
JO - Banach Center Publications
PY - 2008
VL - 79
IS - 1
SP - 197
EP - 202
AB - 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.
LA - eng
KW - partially ordered Banach spaces; Ben-Israel–Charnes spaces
UR - http://eudml.org/doc/286205
ER -