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\title{HW 6}
\author{Optimization methods 2011}

\begin{document}

\begin{enumerate}
 \item 13.5, 13.9 (graph the solution), 15.3
\item
Find
$$
\min_{x\in R_2} f(x), ~~f=x_1^2 + x_2^2, \mbox{ subject to } x_1-x_2=1
$$
using
\begin{enumerate}
 \item Quadratic penalty, take $\mu= 1, 10, 50$
 \item Absolute value (non-smooth) penalty, take $\mu= 1, 10, 50$
 \item Augmented Lagrangian, start with the point $\lambda_0=0, ~ \mu_0=1 $
\end{enumerate}

\end{enumerate}


\end{document}
