A primal-infeasible interior point algorithm for linearly constrained convex programming

In this paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. A positive primal-infeasible dual-feasible point can be taken as the starting point of this algorithm in a large region. At each iterates it requires to solve approximately a nonlinear system. The polynomial complexity of the algorithm is obtained. It is shown that, after finite iterations a sufficiently good approximation to the optimal point is found, or there is no optimal point in a large region.