AN ALGORITHMS TO DETERMINE BOUNDEDNESS OF QUADRATICALLY CONSTRAINED CONVEX QUADRATIC PROGRAMS

In this paper we present an algorithm which can be used to determine w hether or not a convex quadratic objective function is bounded from be low over a feasible region defined by convex quadratic constraints. If there are m constraints and n variables, the algorithm terminates aft er at most min{m - 1, n - 1} iterations. Each iteration requires the i dentification of implicit equality constraints in a system of homogene ous linear inequality and equality constraints, and the identification can be completed by the solution of linear programmes. In addition, t he algorithm has the advantage of providing a mechanism to reduce both the number of constraints and the dimension of the problem.