A wide neighborhood primal-dual interior-point algorithm for a class of convex programming

Abstract

This paper presents a new primal-dual interior-point algorithm with reduced potential function for a class of convex programming, based on the ideas of that method for solving linear programming. The new algorithm chooses the classical Newton direction as iteration direction and its iteration stepsize is determined by potential function. As the search directions Δx and Δs aren't orthogonal any more, the complexity analysis of this method is different from that of linear programming, correspondingly. Under a scaled Lipschitz condition, the algorithm is proved to possess O(nL) iteration-complexity bounds © 2008 Springer-Verlag Berlin Heidelberg.