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Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations

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Abstract

In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.

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Authors and Affiliations

  1. Qingdao, P.R. China

    Shou-Qiang Du

  2. Shanghai, P.R. China

    Yan Gao

  3. College of Mathematics, Qingdao University, Qingdao, 266071, P.R. China

    Shou-Qiang Du

  4. School of Management, University of Shanghai for Science and Technology, Jungong Road 516, Shanghai, 200093, P.R. China

    Yan Gao

Authors
  1. Shou-Qiang Du
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  2. Yan Gao
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Correspondence to Shou-Qiang Du.

Additional information

Supported by National Science Foundation of China (10671126), Shanghai Leading Discipline Project (S30501), Innovation Program of Shanghai Education Commission (10YZ99), and Higher Educational Science and Technology Program of Shandong Province (J10LA05).

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Du, SQ., Gao, Y. Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations. Appl Math 56, 481–498 (2011). https://doi.org/10.1007/s10492-011-0027-y

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  • DOI: https://doi.org/10.1007/s10492-011-0027-y

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