Copositivity conditions for global optimality in indefinite quadratic programming problems

This note generalizes a criterion necessary and sufficient for global optimality in concave quadratic minimization problems, which was derived by Hiriart-Urruty and Lemarechal by means of •-subdifferential calculus. Instead of following their approach which is applicable only to concave objectives, a direct method is specified here which works for general indefinite quadratic objectives. The resulting criterion is reformulated into copositivity conditions, and is put into relation to copositivity conditions for local optimality.