A combination of potential reduction steps and steepest descent steps for solving convex programming problems

This paper studies the possibility of combining interior point strategy with a steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal-dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The O(rootn\ In epsilon\) complexity, of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright (C) 2002 John Wiley Sons, Ltd.