QDN: a variable storage algorithm for unconstrained optimization

The algorithm quasi-discrete Newton (QDN) is presented which essentially uses the preconditioned conjugate gradient method to solve iteratively the linear systems which arise in Newton's method. Directions of negative curvature are obtained and dealt with in an efficient and natural manner. A main feature of QDN is that the amount of storage required is controlled by the choice of the preconditioning matrix. Preliminary numerical experimentation indicates that QDN compares favorably with the now standard secant methods and the standard conjugate gradient methods. 1 table.