G. Wanka : A New Theorem od the Alternative - A Location Approach

Author(s) :

G. Wanka

Title :

A New Theorem od the Alternative - A Location Approach

Electronic source:

application/pdf

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-5, 1998

Mathematics Subject Classification :

41A63 [ Multidimensional approximation problems ]

Abstract :

By means of a location approach there is given a new new method to obtain theorems of the alternative. This consists in associating a location problem to the considered orginal system of linear inequalities. There is introduced a dual optimization problem and strong duality is established. From the dual problem there is derived a second system of equationes and inequaalities and for both systems the duality and solvability properties allow to conclude a gerneral theorem of the alternative. The assigned locatione problem includes weigtheing factors and powers of the norms. These weighting factors and exponents may be considered as parameters appearinmg ind the theorem of the alternative, which therefore represents a whole class of theorems of the alternative. The presented theorem of the alternative for linear inequalities.

Keywords :

theorem of the alternative, location problem, duality

Language :

english

Publication time :

3/1998