Can someone explain the differences between the relative error definitions used as an objective function in a constrained optimization problem? I am trying to understand why I get different values of $\rho \in \mathbb{R}^{3}$ using fmincon in MATLAB.

The first is normalized by the sum of the two complex valued functions $Z(\omega),\hat{Z}(\rho,\omega) \in \mathbb{C}$ \begin{equation} \underset{\rho}{\text{arg min}}\quad \frac{\left\lVert Z(\omega) - \hat{Z}(\rho,\omega)\right\rVert^{2}}{\left\lVert Z(\omega) + \hat{Z}(\rho,\omega) \right\rVert^{2}}, \end{equation} while the second is normalized by only one of them \begin{equation} \underset{\rho}{\text{arg min}}\quad \frac{\left\lVert Z(\omega) - \hat{Z}(\rho,\omega) \right\rVert^{2}}{\left\lVert Z(\omega) \right\rVert^{2}}, \end{equation} where $\left\lVert \cdot \right\rVert^{2}$ is the $L^{2}$-norm over frequency $\omega$.

Does this have something to do with the complex functions $Z(\omega),\hat{Z}(\rho,\omega) \in \mathbb{C}$ inside the norm?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.