$4\mathrm{.}3$ Program the trust$-$region method based on Algorithm $7\mathrm{.}2.$ Choose $B_k$ to be the exact Hessian, and use it to minimize the function

minf$(x)={\displaystyle \underset{i=1}{\overset{n}{}}}[(1-x_{2i-1}{)}^2+10(x_{2i}-x_{2i-1}^2{)}^2]$

with $n=10.$ Experiment with the starting point and the stopping test for the CG iteration. Repeat the computation with $n=50.$

Your program should indicate, at every iteration, whether Algorithm $7\mathrm{.}2$ encountered negative curvature, reached the trust$-$region boundary, or met the stopping test.h