Implementations of Affine Scaling Methods: Approximate Solutions of Systems of Linear Equations Using Preconditioned Conjugate Gradient Methods

The conjugate gradient method has been proposed for solving system of linear equations arising at each iteration of interior point methods. This paper studies several problems associated with developing such implementations. This includes development of a termination criteria, computation of an effective preconditioner, and the lack of positive definiteness of the matrix.

INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.