The Trust region affine interior point algorithm for convex and nonconvex quadratic programming
Résumé
We 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. We show that, under some nondegeneracy hypothesis, the sequence of points converges to a stationary point at a linear rate. We obtain also an asymptotic linear convergence rate for the cost that depends only on the dimension of the problem. Then we show that, provided some modifications are added to the basic algorithm, the method has a good numerical behaviour.