Generation of conjugate directions for unconstrained minimization without derivatives

Nazareth, Larry

doi:10.1090/S0025-5718-1976-0398100-2

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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