Accession Number : ADA111627

Title :   A Procedure for Computing Forward-Difference Intervals for Numerical Optimization.

Descriptive Note : Technical rept.,


Personal Author(s) : Gill,P. E. ; Murray,W. ; Saunders,M. A. ; Wright,M. H.

Report Date : DEC 1981

Pagination or Media Count : 31

Abstract : When minimizing a smooth nonlinear function whose derivatives are not available, a popular approach is to use a gradient method with a finite-difference approximation substituted for the exact gradient. In order for such a method to be effective, it must be possible to compute 'good' derivative approximations without requiring a large number of function evaluations. Certain 'standard' choices for the finite-difference interval may lead to poor derivative approximations for badly scaled problems. We present an algorithm for computing a set of intervals to be used in a forward-difference approximation of the gradient, and describe its implementation as a transportable Fortran subroutine.

Descriptors :   *Computations, *Numerical analysis, *Optimization, *Finite difference theory, Intervals, Functions, Approximation(Mathematics), Fortran, Subroutines, Computer programs, Algorithms, Gradients

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE