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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A quasi-Newton method with no derivatives
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by John Greenstadt PDF
Math. Comp. 26 (1972), 145-166 Request permission

Abstract:

The Davidon formula and others of the “quasi-Newton” class, which are used in the unconstrained minimization of a function $f$, provide a (generally) convergent sequence of approximations to the Hessian of $f$. These formulas, however, require the independent calculation of the gradient of $f$. In this paper, a set of new formulas is derived—using a previously described variational approach—which successively approximates the gradient as well as the Hessian, and uses only function values. These formulas are incorporated into an algorithm which, although still crude, works quite well for various standard test functions. Extensive numerical results are presented.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 145-166
  • MSC: Primary 65K05
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0305592-X
  • MathSciNet review: 0305592