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A nonmonotone Levenberg–Marquardt method for nonlinear complementarity problems under local error bound

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Abstract

In this paper, we propose a new Levenberg–Marquardt algorithm for nonlinear complementarity problems. The algorithm is based on a semismooth equation reformulation of the complementarity problem using the FB function. To obtain the global convergence, we use a modified nonmonotone line search rule. Under the local error bound assumption, which is weaker than the nonsingularity condition, we get the local superlinear/quadratic convergence of the algorithm. Some numerical examples are given to illustrate the performance and efficiency of the presented algorithm.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing, 350300, People’s Republic of China

    Bin Fan

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  1. Bin Fan
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Correspondence to Bin Fan.

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Communicated by José Mario Martínez.

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Fan, B. A nonmonotone Levenberg–Marquardt method for nonlinear complementarity problems under local error bound. Comp. Appl. Math. 36, 185–202 (2017). https://doi.org/10.1007/s40314-015-0222-7

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  • DOI: https://doi.org/10.1007/s40314-015-0222-7

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