Mathematical Programming

, Volume 18, Issue 1, pp 31–40 | Cite as

Curvilinear path steplength algorithms for minimization which use directions of negative curvature

  • Donald Goldfarb
Article
Received:
Revised:

Abstract

The Armijo and Goldstein step-size rules are modified to allow steps along a curvilinear path of the formx(α) + x + αs + α2d, wherex is the current estimate of the minimum,s is a descent direction andd is a nonascent direction of negative curvature. By using directions of negative curvature when they exist, we are able to prove, under fairly mild assumptions, that the sequences of iterates produced by these algorithms converge to stationary points at which the Hessian matrix of the objective function is positive semidefinite.

Key words

Step-size Procedures Line Search Gradient Methods Unconstrained Minimization Negative Curvature 
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Copyright information

© The Mathematical Programming Society 1980

Authors and Affiliations

  • Donald Goldfarb
    • 1
  1. 1.City College of the City University of New YorkNew YorkUSA

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