On two questions of optimization theory concerning quadratic mappings

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. © 2011 Springer-Verlag.