FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 4, PAGES 1019-1034
L. I. Krechetov
Abstract
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The property of almost monotonicity for the non-singular
irreducible M-matrix is specified. In its existing form the
property means that the result of application of the above
matrix to a vector is either the zero vector or a vector with at
least one component positive and one component negative. In this
paper the positive and the negative components are explicitly
indicated. As an application, a criterion of Pareto-extremality
for a vector function with essentially non-negative matrix of
partial derivatives is derived. The criterion is a counterpart
of the classical Fermat theorem on vanishing of the derivative in
an extremal point of a function. The proofs are based on
geometric properties of $n$ -dimensional simplex described in two
lemmas of independent nature.
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Last modified: April 10, 2003