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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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Generation of conjugate directions for unconstrained minimization without derivatives
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by Larry Nazareth PDF
Math. Comp. 30 (1976), 115-131 Request permission

Abstract:

We analyze a technique for unconstrained minimization without derivatives. This stems from two theorems proved by M. J. D. Powell. A particular version, which we consider in detail, is related to the Jacobi process for finding the eigensystem of a symmetric matrix, and the two processes, although different, help to illuminate one another. We study convergence of the search directions to mutual conjugacy, cases when cycling occurs and identify a broad class of ’cyclic patterns’ for which convergence to mutual conjugacy is proven.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 115-131
  • MSC: Primary 65K05
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0398100-2
  • MathSciNet review: 0398100