A polynomial path following algorithm for convex programming

In this paper, based on combined homotopy interior point method we propose an interior point algorithm for convex nonlinear programming. The algorithm ensures that the obtained iterative points are interior points of the feasible set in terms of the technique of β  -cone neighborhood. We establish the global convergence of the algorithm. Furthermore, it is shown that the algorithm has O(nL) iteration complexity. The preliminary numerical experiments indicate that the algorithm is efficient.