Software Performance on Nonlinear Least-Squares Problems

Abstract

This paper presents numerical results for a large and varied set of problems using software that is widely available and has under gone extensive testing. The algorithms implemented in this software include Newton-based line search and trust-region methods for unconstrained optimization, as well as Gauss-Newton, Levenberg Marquardt, and special quasi-Newton methods for nonlinear least squares. Rather than give a critical assessment of the software itself, our original purpose was to use the best available software to compare the underlying algorithms, to identify classes of problems for each method on which the performance is either very good or very poor, and to provide benchmarks for future work in nonlinear least squares and unconstrained optimization. The variability in the results made it impossible to meet either of the first two goals; however the results are significant as a step toward explaining why these aims are so difficult to achieve.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1988
Accession Number
ADA201879

Entities

People

  • Christina Fraley

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computations
  • Computer Programming
  • Computer Programs
  • Computers
  • Equations
  • Jet Propulsion
  • Least Squares Method
  • Linear Accelerators
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Square Roots

Readers

  • Operations Research
  • Systems Analysis and Design