Abstract
It is known that the conjugate-gradient algorithm is at least as good as the steepest-descent algorithm for minimizing quadratic functions. It is shown here that the conjugate-gradient algorithm is actually superior to the steepest-descent algorithm in that, in the generic case, at each iteration it yields a lower cost than does the steepest-descent algorithm, when both start at the same point.
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References
Luenberger, D. G.,Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973.
Langlois, W. E.,Conditions for Termination of the Method of Steepest Descent After a Finite Number of Iterations, IBM Journal of Research and Development, Vol. 10, pp. 98–99, 1966.
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Communicated by D. Q. Mayne
Thanks are due to Professor R. W. Sargent, Imperial College, London, England, for suggestions concerning presentation.
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Allwright, J.C. Conjugate gradient versus steepest descent. J Optim Theory Appl 20, 129–134 (1976). https://doi.org/10.1007/BF00933351
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DOI: https://doi.org/10.1007/BF00933351