Table I.
Case |
Assumption |
Conclusion |
Proof |
I. |
either or for some and in the latter case for at least one index among the components of s_{k} 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 |
takes on its minimum on K |
Lemma 5.1 |
III. |
For some vector the following hold: |
the nonlinear part of can be shortened |
Theorem 6.1 |
IV. |
the linear part of can be contracted |
Theorem 7.3 |