Case |
Assumption |
Conclusion |
Proof |
I. |
either or for some and in the latter case for at least one index among the components of sk there occur one(s) with zero and other(s) with positive value |
is not bounded from below on K
|
Theorem 4.1 |
II. |
for every where

|
takes on its minimum on K
|
Lemma 5.1 |
III. |
For some vector the following hold:
a) ;
b) for every index either sk >> 0 or sk = 0;
c) sk >> 0 is fulfilled for at least one index ; |
the nonlinear part of can be shortened |
Theorem 6.1 |
IV. |
For some vector the following hold:
a) ;
b) sk >> 0 for every ; |
can be reduced to a linear function
|
Theorem 6.2 |