Abstract
In this paper we present solutions of two open problems from the theory of quadratic mappings arising from the optimization theory and formulated by Hiriart-Urruty (SIAM Rev 49(2):255–273, 2007). The first problem is concerned with the non-triviality of the set of common zeroes of finitely many of quadratic forms. The second problem deals with the positivity of the maximum of finitely many of quadratic forms.
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