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\title{HW 5}
\author{Optimization methods 2011}
\date{}
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\maketitle
\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=1/2,  1, 10 $ (you may use other values)
 \item augmented Lagrangian, start with the point $\lambda_0=0, ~ \mu_0=1 $.
\end{enumerate}

\end{enumerate}


\end{document}
