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On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints

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Abstract

In this paper, we present new convergence results of augmented Lagrangian methods for mathematical programs with complementarity constraints (MPCC). Modified augmented Lagrangian methods based on four different algorithmic strategies are considered for the constrained nonconvex optimization reformulation of MPCC. We show that the convergence to a global optimal solution of the problem can be ensured without requiring the boundedness condition of the multipliers.

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Authors and Affiliations

  1. Department of Management Science, School of Management, Fudan University, 200433, Shanghai, People’s Republic of China

    H. Z. Luo, X. L. Sun & Y. F. Xu

  2. Department of Applied Mathematics, Zhejiang University of Technology, 310032, Hangzhou, Zhejiang, People’s Republic of China

    H. Z. Luo

  3. Department of Mathematics, Hangzhou Dianzi University, 310018, Hangzhou, Zhejiang, People’s Republic of China

    H. X. Wu

Authors
  1. H. Z. Luo
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  2. X. L. Sun
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  3. Y. F. Xu
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  4. H. X. Wu
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Correspondence to X. L. Sun.

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Luo, H.Z., Sun, X.L., Xu, Y.F. et al. On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints. J Glob Optim 46, 217–232 (2010). https://doi.org/10.1007/s10898-009-9419-x

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  • DOI: https://doi.org/10.1007/s10898-009-9419-x

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