Geodesic
Nonnegativity of Quadratic Forms on Intersections of Quadrics and Quadratic Maps
Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 163-174.

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The question of the nonnegativity of quadratic forms on intersections of quadratic cones is considered. An answer is given in terms of Lagrange multipliers of the quadratic forms under consideration.
Keywords: quadratic form, quadratic cone, quadratic map, regular zero of a quadratic function, abnormal point, bilinear map, Sard's theorem. 
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A. V. Arutyunov. Nonnegativity of Quadratic Forms on Intersections of Quadrics and Quadratic Maps. Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 163-174. http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a0/

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