Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming

In this paper, we propose primal-dual potential-reduction algorithms which can start from an infeasible interior point. We rst describe two such algorithms and show that both are polynomial-time bounded. One of the algorithms decreases the Tanabe-Todd-Ye primal-dual potential function by a constant at each iteration under the condition that the duality gap decreases by at most the same ratio as the infeasibility. The other reduces a new potential function, which has one more term in the Tanabe-Todd-Ye potential function, by a xed constant at each iteration without any other conditions on the step size. Finally, we describe modiications of these methods (incorporating centering steps) which dramatically decrease their computational complexity. Our algorithms also extend to the case of monotone linear complementarity problems.