Abstract
This paper presents a successive element correction algorithm and a secant modification of this algorithm. The new algorithms are designed to use the gradient evaluations as efficiently as possible in forming the approximate Hessian. The estimates of theq-convergence andr-convergence rates show that the new algorithms may have good local convergence properties. Some restricted numerical results and comparisons with some previously established algorithms suggest that the new algorithms may be efficient in practice.
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Communicated by R. A. Tapia
The author would like to thank T. F. Coleman for his many important and helpful suggestions and corrections on the preliminary draft of this paper. The author is also grateful to R. A. Tapia, the editors, and the referees for helpful suggestions and corrections.
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Li, G.Y. Successive element correction algorithms for sparse unconstrained optimization. J Optim Theory Appl 77, 523–543 (1993). https://doi.org/10.1007/BF00940448
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DOI: https://doi.org/10.1007/BF00940448