I am trying to get the standard form of a quadratic program. The general form is as follows
I don't understand how to get the matrix $a$ (for the coefficients of the inequality constraints) of the following specific problem:
Please can anyone tell me how to write the matrix $a$ and matrix $b$ this problem(as shown in the general form) in order to get the standard form of this quadratic problem?
Using the representation of the picture you can write each constraint as a product of two vectors. For instance the first inequality:
$$ 3x_1+4x_2-2x_3= \left(\begin{array}{} 3 & 4 & -2 \end{array}\right)\cdot \begin{pmatrix}{} x_1 \\ x_2 \\ x_3 \\ \end{pmatrix}\leq 10$$
But if you want to use one coefficient matrix $A$ for all equations we have to add slack variables (+$s_i$) and surplus variables ($-s_i$), since all constraints have to be equations.
$$\underbrace{\begin{pmatrix}{} 3&4&-2&1&0&0&0&0 \\ -3&2&1&0&-1&0&0&0 \\ 2&3&4&0&0&0&0&0 \\ 1&0&0&0&0&1&0&0\\ 0&1&0&0&0&0&1&0\\ 0&0&1&0&0&0&0&1\\\end{pmatrix}}_{A}\cdot \underbrace{\begin{pmatrix}{} x_1 \\ x_2 \\ x_3 \\ s_1 \\ s_2\\ s_3\\ s_2\\ s_5 \end{pmatrix}}_{x}=\underbrace{\begin{pmatrix}{}10 \\ 2 \\ 5 \\ 5\\ 5 \\ 5 \end{pmatrix}}_{b}$$
The second constraint is $-3x_1+2x_2+x_3-s_2=2$. You just have to know how to multiply a matrix by a vector.
And finally the non-negativity condition: $x_i,s_i\geq 0$