Nonsymmetric potential-reduction methods for general cones

In this paper we propose two new nonsymmetric primal-dual potential-reduction methods for conic problems. Both methods are based on {\em primal-dual lifting}. This procedure allows to construct a strictly feasible primal-dual pair linked by an exact {\em scaling} relation even if the cones are not symmetric. It is important that all necessary elements of our … Read more

Towards nonsymmetric conic optimization

In this paper we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cones. We suggest using the primal correction process to find a {\em scaling point}. This point is used to compute a strictly feasible primal-dual pair by simple projection. Then, we define … Read more


We study the limiting properties of the affine-scaling directions for linear programming problems. The worst-case angle between the affine-scaling directions and the objective function vector provides an interesting measure that has been very helpful in convergence analyses and in understanding the behaviour of various interior-point algorithms. We establish new relations between this measure and some … Read more