On affine scaling algorithms for nonconvex quadratic programming

The paper investigates the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex-indefinite or negative definite-quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a ‘hard’ problem, it shows that the problem with an ellipsoidal constraint is ‘easy’. When the ‘hard’ QP is solved by successively solving the ‘easy’ QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.