First and second-order derivatives for CP and INDSCAL

In this paper we provide the means to analyse the second-order differential structure of optimization functions concerning CANDECOMP/PARAFAC and INDSCAL. Closed-form formulas are given under two types of constraint: unit-length columns or orthonormality of two of the three component matrices. Some numerical problems that might occur during the computation of the Jacobian and Hessian matrices are addressed. The use of these matrices is illustrated in three applications.