Lagrangian Stability and Global Optimality in Nonconvex Quadratic Minimization over Euclidean Balls and Spheres

We prove in this paper the stability of the Lagrangian duality in nonconvex quadratic minimization over Euclidean balls and spheres. As direct consequences we state both global optimality conditions in these problems and detailed descriptions of the structure of their solution sets. These results are essential for devising solution algorithms.