(A) perform a conjugate gradient (CG) iteration with a predefined first order derivative vector and a predefined second order derivative matrix, wherein performance of the conjugate gradient iteration updates a CG residual vector, an H-conjugate vector, and a residual weight vector;

(B) update a CG solution vector using a previous CG solution vector, the updated H-conjugate vector, and the updated residual weight vector;

(C) compute an eigenvector of the predefined second order derivative matrix that has a smallest eigenvalue relative to other eigenvalues of other eigenvectors of the predefined second order derivative matrix;

(D) define a basis matrix that includes a previous cubic regularization (CR) solution vector, a previous CR residual vector, the updated CG solution vector, the updated CG residual vector, and the computed eigenvector;

(E) perform a CR iteration to update the previous CR solution vector using the defined basis matrix;

(F) update the previous CR residual vector using the predefined first order derivative vector, the predefined second order derivative matrix, and the updated previous CR solution vector;

(G) repeat (A) through (F) until a stop criterion is satisfied, wherein, on a next iteration of (A) through (F), the previous CG solution vector is the updated CG solution vector, the previous CR residual vector is the updated previous CR residual vector, and the previous CR solution vector is the updated previous CR solution vector; and

output the updated previous CR solution vector for use in solving a nonlinear optimization problem.