Abstract
It has become customary to compare the performance of unconstrained optimization algorithms on families of extended symmetric test functions. In this paper, results are presented which indicate that the performance of the variable metric algorithm on such functions is greatly distorted by rounding errors that destroy the special nature of these functions. A simple method of overcoming this difficulty is demonstrated, and it confirms the theoretical result that the number of iterations required to solve such problems is independent of the dimension.
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Dixon, L. C. W.,Nonlinear Optimization: A Survey, Software for Numerical Mathematics and Its Applications, Edited by D. J. Evans, Academic Press, London, England, pp. 193–218, 1973.
Dixon, L. C. W. andPrice, R. C. Truncated Newton Method for Sparse Unconstrained Optimization Using Automatic Differentiation, Journal of Optimization Theory and Applications, Vol. 60, pp. 261–275, 1989.
Spedicato, E. P.,On a Conjecture of Dixon and Other Topics in Variable Metric Methods, Technical Report SMSIA 75/15, University of Bergamo, 1975.
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This research was supported by the Science and Engineering Research Council.
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Dixon, L.C.W., Mills, D.J. Effect of rounding errors on the variable metric method. J Optim Theory Appl 80, 175–179 (1994). https://doi.org/10.1007/BF02196600
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DOI: https://doi.org/10.1007/BF02196600