In this paper we will deal with primal{dual interior point methods for solving the linear programming problem. We present a short step and a long step path{following primal{dual method and derive polynomial{ time bounds for both methods. The iteration bounds are as usual in the existing literature, namely O(pnL) iterations for the short step, and O(nL) for the long step variant. In the analysis...

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite ...

In the Newton/log-barriermethod,Newton steps are taken for the log-barrier function for a xed value of the barrier parameter until a certain convergence criterion is satis ed. The barrier parameter is then decreased and the Newton process is repeated. A naive analysis indicates that Newton's method does not exhibit superlinear convergence to the minimizer of each instance of the log-barrier fun...