Journal of Optimization Theory and Applications

, Volume 18, Issue 2, pp 187–197

New least-square algorithms

  • W. C. Davidon
Contributed Papers

DOI: 10.1007/BF00935703

Cite this article as:
Davidon, W.C. J Optim Theory Appl (1976) 18: 187. doi:10.1007/BF00935703


New algorithms are presented for approximating the minimum of the sum of squares ofM real and differentiable functions over anN-dimensional space. These algorithms update estimates for the location of a minimum after each one of the functions and its first derivatives are evaluated, in contrast with other least-square algorithms which evaluate allM functions and their derivatives at one point before using any of this information to make an update. These new algorithms give estimates which fluctuate about a minimum rather than converging to it. For many least-square problems, they give an adequate approximation for the solution more quickly than do other algorithms.

Key Words

Least-square methodsvariable-metric methodsgradient methodsnonlinear programming

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • W. C. Davidon
    • 1
  1. 1.Haverford CollegeHaverford