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Applications of nonnegative operators to a class of optimization problems

100%

Sivakumar K.

Banach Center Publications

2008

tom 79

nr 1

197-202

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.

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Intervals of certain classes of Z-matrices

63%

Kannan M., Sivakumar K.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 1

85-93

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

Ograniczanie wyników

1 Banach Center Publications

1 Discussiones Mathematicae - General Algebra and Applications

2 Sivakumar K.

1 Kannan M.

1 2014

1 2008

Wyniki wyszukiwania

Applications of nonnegative operators to a class of optimization problems

Intervals of certain classes of Z-matrices