Direct computation of critical points based on Crout’s elimination and diagonal subset test function

The paper presents the method for direct computation of critical points. A general algorithm for the quadratically convergent extended system formulation is introduced based on an arbitrary subset of the diagonal elements of the upper triangular matrix as a critical point test function. Closed-form solutions for all derivatives on an element level were obtained by using symbolic code generation. An algorithm for the backward automatic differentiation of matrix decomposition is developed for the linearization of the test function at the global level. The proposed algorithm is compared with the formulations based on a determinant and a critical diagonal test function.