Block pivoting and shortcut strategies for detecting copositivity

In recently proposed quadratic optimization algorithms, copositivity detection procedures are frequently employed which deliver a feasible direction yielding a negative value of the considered quadratic form, if the answer is negative. To improve the computational performance of this routine, here (1) recursive characterizations of copositivity are presented which enable efficient reduction of the dimension of the problem using block pivoting techniques, and (2) shortcut strategies are described which are connected with diagonalization.