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:
- 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 :
- Publication time :