Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints

Abstract

For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of ∈-subdifferentials of convex functions and ∈-normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality.