Unboundedness of a convex quadratic function subject to concave and convex quadratic constraints (Q1206605)

Sufficient conditions for a convex quadratic function to be unbounded from above, and to be unbounded from below, over a feasible region defined by both convex and concave quadratic constraints, are given. It is shown that the conditions are necessary for the existence of upper bounds if the constraints are concave. A technique for checking the conditions which requires the solution of a finite number of linear programming problems is also presented.