Generation of conjugate directions for unconstrained minimization without derivatives

Author:
Larry Nazareth

Journal:
Math. Comp. **30** (1976), 115-131

MSC:
Primary 65K05

DOI:
https://doi.org/10.1090/S0025-5718-1976-0398100-2

MathSciNet review:
0398100

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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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DOI:
https://doi.org/10.1090/S0025-5718-1976-0398100-2

Article copyright:
© Copyright 1976
American Mathematical Society