Primal-dual potential reduction methods for semidefinite programming usingaffine-scaling directions

Primal-dual affine-scaling methods have recently been extended from linear programming to semidefinite programming. We show how to analyze these metho ds in the framework of potential reduction algorithms. The analysis suggest s implementable variants of the methods as 'long step predictor-corrector' algorithms, where the step length is determined by the potential function. A numerical comparison with the potential reduction method of Nesterov and Todd is presented. (C) 1999 Elsevier Science B.V. and IMACS. All rights res erved.