%  file is     s2.tex
{\bf TRUST REGION METHODS} 
\[ \min_{x\in \Re^n}  f(x) \]
Newton's Method (possible indefinite Hessians)\\
model based (at current estimate $x_c$)
\[f(x) \approx \]
\[  m_{c}(x):=
f(x_{c})+g_{c}^{t}(x-x_{c})+\frac{1}{2}(x-x_{c})^{t}B_{c}(x-x_{c})\]
\[ B_c \approx \nabla^2 f(x_{c}),~~ g_c = \nabla f(x_{c}) \]

TRUST REGION SUBPROBLEM
\[ \min q_c(d) := g_c^t d + \frac{1}{2} d^tB_cd \]
\[ \mbox{subject to~} ||D_c d || \leq \delta_c \]
(unlike Newton's method - not scale invariant)