USING COPOSITIVITY FOR GLOBAL OPTIMALITY CRITERIA IN CONCAVE QUADRATIC-PROGRAMMING PROBLEMS

In this note we specify a necessary and sufficient condition for global optimality in concave quadratic minimization problems. Using this condition, it follows that, from the perspective of worst-case complexity of concave quadratic problems, the difference between local and global optimality conditions is not as large as in general. As an essential ingredient, we here use the epsilon-subdifferential calculus via an approach of Hiriart-Urruty and Lemarechal (1990).