Let
be given such that the system of first order
necessary conditions is satisfied, i.e. the relations (1.2-1.4),
(2.2-2.4) and
are fulfilled. Now we state
second order conditions, which imply local optimality of .
For this purpose, we need the second order derivative of
with respect to ,

(SSC) There exist positive and such that

and

It is known that (SSC) implies local optimality of in a neighborhood of , see [4]. In our example, we shall verify a slightly stronger condition. We require (2.7) for all , which satisfy only (2.8-2.9).

2003-01-25