Abstract
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 theε-subdifferential calculus via an approach of Hiriart-Urruty and Lemarechal (1990).
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Danninger, G., Bomze, I.M. Using copositivity for global optimality criteria in concave quadratic programming problems. Mathematical Programming 62, 575–580 (1993). https://doi.org/10.1007/BF01585185
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DOI: https://doi.org/10.1007/BF01585185