Adequate approach of IPMs for linearly constrained convex optimization

Abstract

In this work, a class of primal-dual interior point methods (IPMs) for solving linearly constrained convex optimization problems is presented. It is a weighted short-step primal-dual interior point algorithm. The proposed algorithm uses at each iteration only full-Newton step where is no calculation of the step size with a quadratic rate of convergence. We analyze a small-update version and we obtain the best-known iteration bound which is as good as the bound for the linear optimization analogue. Finally, some numerical results are reported to show the practical performance of the algorithm with different parameters.