A widely convergent minimization algorithm with quadratic termination property

  • Giulio Treccani
Mathematical Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3)


We have constructed a DSDS whose properties imply the convergence of a conjugate gradient method, which is a modification of the Fletcher and Reeves method and has the quadratic termination property.

The convergence is global for functions continuously differentiable, bounded from below, having bounded level sets and one and only one critical point.

However these assumptions are not restrictive, since if the function is simply continuously differentiable, the algorithm converges to a local minimum point if the initial point is chosen in any bounded level set containing one and only critical point.


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  1. 1.
    G.P. Szego and G. Treccani: Semigruppi di Trasformaioni Multivoche in Symposia Mathematica, Vol.VI, Academic Press, London, New York, 1971, pp.287–307.Google Scholar
  2. 2.
    G.P. Szego and G. Treccani: Axiomatization of minimization algorithms and a new conjugate gradient method in G. Szego "Minimization Algorithms", 1972, Academic Press,Inc. New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • Giulio Treccani
    • 1
  1. 1.Università Di GenovaItaly

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