% file is s16a.tex
{\bf LOCAL-NONGLOBAL MINIMA}\\
(extension of results of Mario Martinez)

{\bf LEMMA} 
Suppose that $y^*$ is a local-nonglobal minimizer of (P) and suppose
that the pencil $B-\lambda C$ is regular and that the
constraint qualification
\[
Cy^* \neq 0
\]
holds. Then
\[
\lambda_{n-1}(B-\lambda^*C) > 0 > \lambda_{n}(B-\lambda^*C).
\]

There are at most two local-nonglobal minima.\\
The existence of lngm implies easy case.\\
A local duality theory exists.