The trust region affine interior point algorithm for convex and nonconvex quadratic programming

The authors study from a theoretical and numerical point of view an interior point algorithm for quadratic QP using a trust region idea, formulated by Ye and Tse. They show that, under a nondegeneracy hypothesis, the algorithm converges globally in the convex case. For a nonconvex problem, under a mild additional hypothesis, the sequence of points converges to a stationary point. The authors obtain also an asymptotic linear convergence rate for the cost that depends only on the dimension of the problem. Then they show that, provided some modifications are added to the basic algorithm, the method has a good numerical behaviour.