Convergence theory for the structured BFGS secant method with an application to nonlinear least squares

In 1981, Dennis and Walker developed a convergence theory for structured secant methods which included the PSB and the DFP secant methods but not the straightforward structured version of the BFGS secant method. Here the authors fill this gap in the theory by establishing a convergence theory for th...

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Bibliographic Details
Published in:Journal of optimization theory and applications 1989-05, Vol.61 (2), p.161-178
Main Authors: DENNIS, J. E. JR, MARTINEZ, H. J, TAPIA, R. A
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Optimization. Search problems
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Summary:In 1981, Dennis and Walker developed a convergence theory for structured secant methods which included the PSB and the DFP secant methods but not the straightforward structured version of the BFGS secant method. Here the authors fill this gap in the theory by establishing a convergence theory for the structured BFGS secant method. A direct application of new theory gives the first proof of local and q-superlinear convergence of the important structured BFGS secant method for the nonlinear least-squares problem, which is used by Dennis, Gay, and Welsh in the current version of the popular and successful NL2SOL code.
ISSN:0022-3239
1573-2878
DOI:10.1007/BF00962795