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{\Large \bf Howework assignment \# 2
}
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1. Derive and solve the system of necessary conditions for the optimization problems:
\begin{equation}
Problem (i): ~~~\min_{\Bx} \Bx^T G \Bx, ~~~~ subject~ to ~~ A_i \Bx \geq  \Bb_i
\end{equation}
where
\begin{equation}
G=\pmatrix{
2 & 1 & 1 \cr
2 & 2 & -1 \cr
1 & -1 & 2 \cr
}
\end{equation}
and

\begin{eqnarray}\label{}
A_1=\left (\matrix{ 1 & 1 & 1 \cr}\right ), ~~ b_1=1 \\
A_2=\left (\matrix{ 1 & 1 & 1 \cr}\right ), ~~ b_1=-1 \\
A_3=
\pmatrix{
1 & 0 & 1 \cr
0 & 1 & 1 \cr
}, ~~b_3=\left (\matrix{
1\cr
-1\cr
}\right )
\end{eqnarray}
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2. Formulate the dual problems and  analyse them. 







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