This technical report provides supplementary information for the optimization problems defined for Stable Estimator of Dynamical Systems (SEDS). Reading of this report is not necessary for researchers who only want to use SEDS learning algorithm. The report is aimed at helping those persons who want to develop SEDS, or to write their own optimization program. All the formulations reported here are developed for SEDS models; however, they can also be used for general Gaussian Mixture Model (GMM) formulations. In the case of the latter, they should be slightly modified to consider the general form of GMM. Hopefully, the report should be clear enough to help readers in that.