TRUST REGION PROBLEMS (known results) 

\begin{enumerate}
\item[]
Levenberg 1944, Marquadt 1963 (Least Squares)
\item[]
Forsythe and Golub, 1965
\item[]
Goldfeld, Quandt, and Trotter, 1966
\item[]
Gander, 1981
\item[]
Sorensen, 1982
\item[]
More and Sorensen, 1983
\item[]
Gander, Golub, and Von Matt, 1989
\end{enumerate}

\[  \min_{x^tx=1} (\max)~~ x^tBx - 2 \eta^tx   \]

\[ {\rm Lagrangian} ~~~ L(x,\lambda) = x^tBx - 2 \eta^t x
                               -\lambda(x^tx-1)  \]

\[  (B-\lambda I)x - \eta = 0 \]
$\lambda \in \Lambda $ Lagrange multipliers \\
$x \in S_{\mu} (\lambda) $  stationary points