On the convergence of the Davidon–Fletcher–Powell algorithm for unconstrained optimization when there are only two variables

On the convergence of the Davidon–Fletcher–Powell algorithm for unconstrained optimization when there are only two variables

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Article ID: iaor2001994
Country: Germany
Volume: 87
Issue: 2
Start Page Number: 281
End Page Number: 301
Publication Date: Jan 2000
Journal: Mathematical Programming
Authors:
Abstract:

Let the DFP algorithm for unconstrained optimization be applied to an objective function that has continuous second derivatives and bounded level sets, where each line search finds the first local minimum. It is proved that the calculated gradients are not bounded away from zero if there are only two variables. The new feature of this work is that there is no need for the objective function to be convex.

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