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A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

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  • Li, Jianling
  • Huang, Renshuai
  • Jian, Jinbao

Abstract

In this paper, based on the smoothing techniques and the working set techniques, a QP-free algorithm for mathematical programs with equilibrium constraints (MPEC for short) is presented. Firstly, by Fischer–Burmeister function and smoothing techniques, the discussed problem is approximated by a smooth constrained optimization problem. Secondly, the working set, which is used to construct systems of linear equations, is generated by pivoting operation. At each iteration, the search direction is yielded by solving two or three systems of equations with the same coefficient matrix. Under mild conditions, the global convergence and superlinear convergence are shown. Moreover, we can conclude that the current iterative point is an exact stationary point of the discussed problem if the proposed algorithm stops after finite iterations. Finally, preliminary numerical results are reported.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:885-903
    DOI: 10.1016/j.amc.2015.07.081
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    References listed on IDEAS

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    1. 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.
    2. H. Luo & X. Sun & Y. Xu & H. Wu, 2010. "On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints," Journal of Global Optimization, Springer, vol. 46(2), pages 217-232, February.
    3. 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.
    4. Jian, Jin-Bao & Pan, Hua-Qin & Tang, Chun-Ming & Li, Jian-Ling, 2015. "A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 560-578.
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    Cited by:

    1. Qingna Li & Zhen Li & Alain Zemkoho, 2022. "Bilevel hyperparameter optimization for support vector classification: theoretical analysis and a solution method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(3), pages 315-350, December.
    2. Li, Jianling & Yang, Zhenping, 2018. "A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 52-72.

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