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On the convergence of sequential minimization algorithms

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Abstract

This note discusses the conditions for convergence of algorithms for finding the minimum of a function of several variables which are based on solving a sequence of one-variable minimization problems. Theorems are given which contrast the weakest conditions for convergence of gradient-related algorithms with those for more general algorithms, including those which minimize in turn along a sequence of uniformly linearly independent search directions.

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Authors and Affiliations

  1. Department of Chemical Engineering and Chemical Techology, Imperial College, London, England

    R. W. H. Sargent (Professor) & D. J. Sebastian (Graduate student)

Authors
  1. R. W. H. Sargent
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  2. D. J. Sebastian
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Additional information

Communicated by M. R. Hestenes

The senior author benefited greatly from discussion of this problem with various participants at the NATO Summer School on Mathematical Programming in Theory and Practice held at Figueira da Foz, Portugal, June 1972, and in particular with M. J. D. Powell, who, in continuing correspondence, has produced a series of examples and counterexamples for various versions of the theorems.

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Sargent, R.W.H., Sebastian, D.J. On the convergence of sequential minimization algorithms. J Optim Theory Appl 12, 567–575 (1973). https://doi.org/10.1007/BF00934779

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