Applications of nonnegative operators to a class of optimization problems

• Autorzy: K. C. Sivakumar
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 90C48: Programming in abstract spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 79
• Numer: 1
• Strony: 197-202

Daty

wydano

2008

Twórcy

autor

K. C. Sivakumar

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Identyfikatory

DOI

10.4064/bc79-0-16