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\title{Optimization methods. Fall 2011. HW-2 }
\author{Andrej Cherkaev}
\date{Due day: Monday September 10}
\maketitle
Minimize the function
$$
f(x_1, x_2) =(x^4+x^2+y^2+1.2\,x\,(y+1)^{1.4}+1)^{0.7}
$$
by 
\begin{enumerate}
\item Steepest descent method
\item Newton method
\item Modified Newton method (Levenberg - Marquardt algorithm)
\end{enumerate}
Start from the points $ [1, 0]$ and $[1, -1]$.
Compute four iterations. Discuss your choice of parameters and compare results obtained by these algorithms. 

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