On the local convergence of a derivative‐free algorithm for least‐squares minimization

On the local convergence of a derivative‐free algorithm for least‐squares minimization

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Article ID: iaor20122779
Volume: 51
Issue: 2
Start Page Number: 481
End Page Number: 507
Publication Date: Mar 2012
Journal: Computational Optimization and Applications
Authors: ,
Keywords: heuristics
Abstract:

In Zhang et al. (2010), we developed a class of derivative‐free algorithms, called DFLS, for least‐squares minimization. Global convergence of the algorithm as well as its excellent numerical performance within a limited computational budget was established and discussed in the same paper. Here we would like to establish the local quadratic convergence of the algorithm for zero residual problems. Asymptotic convergence performance of the algorithm for both zero and nonzero problems is tested. Our numerical experiments indicate that the algorithm is also very promising for achieving high accuracy solutions compared with software packages that do not exploit the special structure of the least‐squares problem or that use finite differences to approximate the gradients.

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