How to rewrite this optimization problem in standard form? Consider the following problem
\begin{eqnarray*}
\underset{y}{\max} & f(y)\\
s.t. & y_{1}A_{1}+y_{2}A_{2}+y_{3}A_{3}+S_{1}=C_{1},\\
 & y_{4}A_{4}+y_{5}A_{5}+y_{6}A_{6}+y_{7}A_{7}+S_{2}=C_{2},\\
 & y_{4}A_{8}+y_{5}A_{9}+y_{6}A_{10}+y_{7}A_{11}+S_{3}=C_{3},\\
 & y_{4}A_{12}+y_{5}A_{13}+y_{6}A_{14}+y_{7}A_{15}+y_{2}A_{16}+y_{3}A_{17}+S_{4}=C_{4},\\
 & S_{1},S_{2},S_{3},S_{4}\succeq0,
\end{eqnarray*}
where $y_{i}$ are scalar variables. How can we rewrite this optimzation
problem in the following form 
\begin{eqnarray*}
\underset{x}{\max} & f(x)\\
s.t. & \sum_{i=1}^{i=m}x_{i}B_{i}+T=D,\\
 & T\succeq0,
\end{eqnarray*}
where $x_{i}$ are scalar variables please? Thanks. 
 A: We have 
$$
{
\begin{array}{rl}
\underset{y}{\max} & f(y)\\
y_1
\left[\begin{array}{cccc}
A_1&0&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&0
\end{array}\right]
+
y_2
\left[\begin{array}{cccc}
A_2&0&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&A_{16}
\end{array}\right]
+
y_3
\left[\begin{array}{cccc}
A_3&0&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&A_{17}
\end{array}\right]
+&
\\
+y_4
\left[\begin{array}{cccc}
0&0&0&0\\0&A_4&0&0\\0&0&A_8&0\\0&0&0&A_{12}
\end{array}\right]
+y_5
\left[\begin{array}{cccc}
0&0&0&0\\0&A_5&0&0\\0&0&A_{9}&0\\0&0&0&A_{13}
\end{array}\right]
+y_6
\left[\begin{array}{cccc}
0&0&0&0\\0&A_6&0&0\\0&0&A_{10}&0\\0&0&0&A_{14}
\end{array}\right]
+
&\\
+y_7
\left[\begin{array}{cccc}
0&0&0&0\\0&A_7&0&0\\0&0&A_{11}&0\\0&0&0&A_{15}
\end{array}\right]
+
\left[\begin{array}{ccc}
S_1&0&0&0\\0&S_2&0&0\\0&0&S_3&0\\0&0&0&S_4
\end{array}\right]
&=
\left[\begin{array}{cccc}
C_1&0&0&0\\0&C_2&0&0\\0&0&C_3&0\\0&0&0&C_4
\end{array}\right]
\\
\left[\begin{array}{ccc}
S_1&0&0&0\\0&S_2&0&0\\0&0&S_3&0\\0&0&0&S_4
\end{array}\right]
&\succeq  0
\end{array}
}
$$
