%  file is   s3.tex
{\bf Special Case}
\[ \mu = \min_{||x || = 1}   x^tBx   \]

\[L(x,\lambda)=x^tBx-\lambda(x^tx-1)~~\mbox{(Lagrangian)}\]
\[ \nabla_x L(x,\lambda) = 0 = Bx-\lambda x \]
\[ \Longrightarrow Bx = \lambda x  ~~\mbox{(eigenvalue-eigenvector)}\]
\[ \mu = x^tBx = \lambda x^tx = \lambda \rightarrow \min \]
We get the smallest eigenvalue.

Nonconvex problem

{\bf IFF}  characterization of {\bf GLOBAL} minimum

Local Minima? (NONE)