An algorithm to determine boundedness of quadratically constrained convex quadratic programs

In this paper we present an algorithm which can be used to determine whether or not a convex quadratic objective function is bounded from below over a feasible region defined by convex quadratic constraints. If there are m constraints and n variables, the algorithm terminates after at most min{m – 1, n – 1} iterations. Each iteration requires the identification of implicit equality constraints in a system of homogeneous linear inequality and equality constraints, and the identification can be completed by the solution of linear programs. In addition, the algorithm has the advantage of providing a mechanism to reduce both the number of constraints and the dimension of the problem.