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A new class of nonmonotone adaptive trust-region methods for nonlinear equations with box constraints

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Abstract

A nonmonotone trust-region method for the solution of nonlinear systems of equations with box constraints is considered. The method differs from existing trust-region methods both in using a new nonmonotonicity strategy in order to accept the current step and a new updating technique for the trust-region-radius. The overall method is shown to be globally convergent. Moreover, when combined with suitable Newton-type search directions, the method preserves the local fast convergence. Numerical results indicate that the new approach is more effective than existing trust-region algorithms.

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Acknowledgements

The author would like to thank Prof. Christian Kanzow for help to prove some Lemmas and Theorems, especially local convergence, and Prof. Stefania Bellavia and Prof. Sandra Pieraccini for providing some of the test examples.

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  1. Department of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran

    Morteza Kimiaei

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  1. Morteza Kimiaei
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Kimiaei, M. A new class of nonmonotone adaptive trust-region methods for nonlinear equations with box constraints. Calcolo 54, 769–812 (2017). https://doi.org/10.1007/s10092-016-0208-x

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