On a Class of Preconditioners for Interior Point Methods

In most primal-dual interior point methods, a sequence of weighted normal equations are solved, where the only change from one problem to the next are the weights and the right hand side. Solving the normal equations alternating between a direct method and an iterative method was introduced in Wang and O'Leary 11]. A class of preconditioners based on a low-rank correction of a Cholesky factorization of a weighted normal equation coeecient matrix was used in 11] and the low-rank correction was based on the diierence of the weights. In Baryamureeba, Steihaug and Zhang 2] it was shown that the low-rank correction should be based on the ratios of the weights to reduce the condition number. The purpose of this paper is to compare the approach in forming the low-rank preconditioners in 2] with the approach by Wang and O'Leary 11, 10]. The theory and numerical testing strongly support the approach by Baryamureeba, Steihaug and Zhang 2].