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The Computer Journal 1967 10(3):293-296; doi:10.1093/comjnl/10.3.293
© 1967 by British Computer Society
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Minimizing a function without calculating derivatives

W. I. Zangwill *

Center for Research in Management Science, University of California, Berekely, California, USA

In an important contribution Powell has suggested an approach for determining the unconstrained minimum of a function of several variables, and determining it without calculating derivatives. This paper studies his approach in some detail. It is first shown by counter-example that his basic method for minimizing a quadratic function in a finite number of iterations contains an error. His modification of his basic method is then simplified, and the simplification proven to converge for strictly convex functions. Finally, we pose a new method not only which converges in a finite number of iterations for a quadratic, but also for which theoretical convergence is established in the strictly convex case.


* Center for Research in Management Science, University of California, Berkeley, California, U.S.A.


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