Abstract.Multi-step quasi-Newton methods for unconstrained optimization were introduced by the authors ([#!7!#,#!8!#]). At each step of the iterative process, these methods employ two polynomials, one to define a path interpolating recent iterates in the variable-space and the other to approximate the gradient as the path is followed. Numerical experiments described in [#!7!#] strongly indicated that several multi-step methods yield substantial computational gains over the standard (one-step) BFGS method. In this paper, we consider how to modify the structure of such methods to provide a more general model of the gradient with the intention of improving the approximation. The model is exploited in utilizing readily computed function values in updating the Hessian approximation. The results of numerical experiments on the new methods are reported and compared with those produced by existing methods.

Received: December 21, 2005

AMS Subject Classification: 65K10

Key Words and Phrases: unconstrained optimization, quasi-Newton methods, multi-step methods

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 2