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An active-set Levenberg–Marquardt method for degenerate nonlinear complementarity problem under local error bound conditions

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Abstract

In this paper, we focus on the identification of the degenerate indices of the nonlinear complementarity problem under the local error bound condition. Under this condition, the complementarity problems may fail to have non-singularity or local uniqueness at its solutions. We present an active-set Levenberg–Marquardt method, which introduces an estimated set to approximate the degenerate indices of the solutions. When near the solution, the degenerate indices will be correctly identified and the original problem will be transformed to a reduced problem. This method has global convergence. Under the local error bound condition, local superlinear convergence is obtained as well.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (11401384), the Scientific Research Foundation for youth teachers of Lixin University of Commerce (2014QNYB17).

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  1. School of Mathematics & Information, Shanghai Lixin University of Commerce, Shanghai, China

    Haodong Yu

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  1. Haodong Yu
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Yu, H. An active-set Levenberg–Marquardt method for degenerate nonlinear complementarity problem under local error bound conditions. J. Appl. Math. Comput. 52, 191–213 (2016). https://doi.org/10.1007/s12190-015-0937-z

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  • DOI: https://doi.org/10.1007/s12190-015-0937-z

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