A polynomial method of weighted centers for convex quadratic programming

A generalization of the weighted central path-following method for convex quadratic programming is presented. This is done by uniting and modifying the main ideas of the weighted central path following method for linear programming and the interior point methods for convex quadratic programming. By means of the linear approximation of the weighted logarithmic barrier function and weighted inscribed ellipsoids, ‘weighted’ trajectories are defined. Each strictly feasible primal-dual point pair defines such a weighted trajectory. The algorithm can start in any strictly feasible point that defines a weighted trajectory, which is followed through the algorithm. This algorithm has the nice feature, that it is not necessary to start the algorithm close to the central path and so additional transformations are not needed. In return, the theoretical complexity of the present algorithm is dependent on the position of the starting point. Polynomiality is proved under the usual mild conditions.