Primal-dual potential reduction methods for semidefinite programming using affine-scaling directions Original Research Article

Primal-dual affine-scaling methods have recently been extended from linear programming to semidefinite programming. We show how to analyze these methods in the framework of potential reduction algorithms. The analysis suggests 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.