Mathematical Programming

, Volume 26, Issue 2, pp 190–212

Truncated-newtono algorithms for large-scale unconstrained optimization


  • Ron S. Dembo
    • School of Organization and ManagementYale University
  • Trond Steihaug
    • Department of Mathematical SciencesRice University

DOI: 10.1007/BF02592055

Cite this article as:
Dembo, R.S. & Steihaug, T. Mathematical Programming (1983) 26: 190. doi:10.1007/BF02592055


We present an algorithm for large-scale unconstrained optimization based onNewton's method. In large-scale optimization, solving the Newton equations at each iteration can be expensive and may not be justified when far from a solution. Instead, an inaccurate solution to the Newton equations is computed using a conjugate gradient method. The resulting algorithm is shown to have strong convergence properties and has the unusual feature that the asymptotic convergence rate is a user specified parameter which can be set to anything between linear and quadratic convergence. Some numerical results on a 916 vriable test problem are given. Finally, we contrast the computational behavior of our algorithm with Newton's method and that of a nonlinear conjugate gradient algorithm.

Key words

Unconstrained OptimizationModified Newton MethodsConjugate Gradient Algorithms

Copyright information

© North-Holland Publishing Company 1983