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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

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