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Convergence Properties of Modified and Partially-Augmented Lagrangian Methods for Mathematical Programs with Complementarity Constraints

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  • H. Z. Luo

    (Fudan University
    Zhejiang University of Technology)

  • X. L. Sun

    (Fudan University)

  • Y. F. Xu

    (Fudan University)

Abstract

We present new convergence properties of partially augmented Lagrangian methods for mathematical programs with complementarity constraints (MPCC). Four modified partially augmented Lagrangian methods for MPCC based on different algorithmic strategies are proposed and analyzed. We show that the convergence of the proposed methods to a B-stationary point of MPCC can be ensured without requiring the boundedness of the multipliers.

Suggested Citation

  • H. Z. Luo & X. L. Sun & Y. F. Xu, 2010. "Convergence Properties of Modified and Partially-Augmented Lagrangian Methods for Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 489-506, June.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-009-9642-0
    DOI: 10.1007/s10957-009-9642-0
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    References listed on IDEAS

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    1. X. M. Hu & D. Ralph, 2004. "Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 365-390, November.
    2. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    3. Gemayqzel Bouza & Georg Still, 2007. "Mathematical Programs with Complementarity Constraints: Convergence Properties of a Smoothing Method," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 467-483, May.
    4. M. A. Diniz-Ehrhardt & M. A. Gomes-Ruggiero & J. M. Martínez & S. A. Santos, 2004. "Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 497-517, December.
    5. Gui-Hua Lin & Masao Fukushima, 2005. "A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints," Annals of Operations Research, Springer, vol. 133(1), pages 63-84, January.
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    Cited by:

    1. H. Wu & H. Luo & J. Yang, 2014. "Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 59(4), pages 695-727, August.
    2. Li, Jianling & Huang, Renshuai & Jian, Jinbao, 2015. "A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 885-903.
    3. Nélida Echebest & María Daniela Sánchez & María Laura Schuverdt, 2016. "Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 92-108, January.
    4. H. Luo & H. Wu & G. Chen, 2012. "On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 599-618, November.
    5. H. Wu & H. Luo, 2012. "Saddle points of general augmented Lagrangians for constrained nonconvex optimization," Journal of Global Optimization, Springer, vol. 53(4), pages 683-697, August.
    6. Huixian Wu & Hezhi Luo & Xiaodong Ding & Guanting Chen, 2013. "Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 56(3), pages 531-558, December.

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