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\title{HW 4}
\author{Optimization Methods Fall 2001}

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\begin{enumerate}
\item Search for a minimum of a function
$$ f(x)=  (x_1-x_2^2)^2 + (1-x_1)^2 + x_2 x_3 + 3 \, x_3^4, \quad x_0= [0, 1, 1]
$$
by

a) Conjugate gradient method (any variant)

b) Quasinewton method (any variant)

Show the history of iterations, compare
\item 5.8 Take n=8, diagonal matrices, eigenvalues are

a) 1, 2, 3, 3, 3, 5, 5, 8.

b) 1,2, 3, 4, 5, 6, 7, 8.

Starting point $x_0=[1,1, \ldots 1]$


\item 5.11
\item 6.2
\item 6.4
\item {\bf Bonus 6.10} If you do not prove it, enjoy the formula's elegancy! 

\end{enumerate}



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