A three step quadratically convergent version of primal affine scaling method

In this paper we consider the primal affine scaling method and show that, asymptotically, a step selection strategy exists which can be viewed as a predictor–corrector method. We investigate two step selection strategies. In the first, one corrector step is taken between each pair of predictor steps, and we call this the 2-step method. In the other two such steps are taken, which we call the 3-step method. We show that the 2-step method attains a superlinear rate of 1.5 while the 3-step method attains a quadratic convergence rate. This improves upon the work of Tsuchiya and Monteiro, who obtained a 2-step rate of 1.3.