How can I infer the cost function from Kruppa's simplified equations
According to the equation(30) in this paper The solution was to reform the Equations from the picture in my question here, and after that(Which the paper mentioned in different, complicated mathematical format) is to take the Frobenius norm to the subtract of newly formulated equations(30) on the paper.

$\rho_{1}/ \phi_{1} = \rho_{2}/ \phi_{2} = \rho_{2}/ \phi_{2}$ where $\rho$ is the numerator of each term of the equations, and $\phi$ is the denominator of each term, now the equation(30) in the paper proposed that: $\rho_{1}* \phi_{2} - \phi_{1}*  \rho_{2} = 0 $ and $\rho_{1}* \phi_{3} - \phi_{1}*  \rho_{3} = 0 $ now taking the Frobenius norm $\parallel.\parallel_{fro} $ for the two equations yields two values, Thus the cost function is the sum of this values.