(Dual problem). Find
The dual problem delivers the highest crossing point for the set
of a collection of affine functions. Hence, it is concave, upper
semi-continuous and may be studied with the means of the propositions
Crossing theorem 2
). In particular,
the following statement directly follows from the proposition
Crossing theorem 1
), the geometrical
interpretation of the (
) and the definition (
(Duality gap and geometric
multipliers). The following alternative takes place.
(="there is no duality gap") then the set of geometric multipliers is equal to
the set of solutions of the problem (
(="there is a duality gap") then the set of geometric multipliers is empty.