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

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.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA111627

Entities

People

  • M. H. Wright
  • Mark A. Saunders
  • P. E. Gill
  • William J. Murray

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Contracts
  • Evolutionary Algorithms
  • Heuristic Methods
  • Intervals
  • Mathematics
  • Optimization
  • Procedures (Computers)
  • Standards
  • Test And Evaluation
  • Transportable

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.