On well-posedness of quadratic minimization problem on ellipsoid and polyhedron (Q2774619)

The authors study the existence of a solution for the quadratic minimization problem on an ellipsoid and on a polyhedron. In the case of an ellipsoid they obtain necessary conditions for the existence of a solution and show that these conditions are sufficient under some additional assumptions. In the case of a polyhedron they find necessary and sufficient conditions for the existence of a solution, and they also show that this condition is sufficient for well-posedness in the sense of Tikhonov.