Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints

For the problem of maximizing a convex quadratic function under convex quad ratic constraints, we derive conditions characterizing a globally optimal s olution. The method consists in exploiting the global optimality conditions , expressed in terms of epsilon -subdifferentials of convex functions and e psilon -normal directions, to convex sets. By specializing the problem of m aximizing a convex function over a convex set, we find explicit conditions for optimality.