Abstract
In previous work, the authors (1993, 1994) developed the concept of multi-step quasi-Newton methods, based on the use of interpolating polynomials determined by data from the m most recent steps. Different methods for parametrizing these polynomials were studied by the authors (1993), and several methods were shown (empirically) to yield substantial gains over the standard (one-step) BFGS method for unconstrained optimization. In this paper, we will consider the issue of how to incorporate function-value information within the framework of such multi-step methods. This is achieved, in the case of two-step methods, through the use of a carefully chosen rational form to interpolate the three most recent iterates. The results of numerical experiments on the new methods are reported.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.