Optimization Algorithm in Discriminant Analysis

Please, I will like to know the optimization objective of Discriminant Analysis and the algorithm that achieves it. Looking through the documentation of fitcdiscr in MATLAB, I do not see anything like this. Please, I will like to know if there is an optimization algorithm in fitcdiscr that minimizes the classification loss or is it just the combination of the misclassification cost and the prior probabilities that get the job done?

Thanks.