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A second-order smooth penalty function algorithm for constrained optimization problems

Author

Listed:
  • Xinsheng Xu
  • Zhiqing Meng
  • Jianwu Sun
  • Liguo Huang
  • Rui Shen

Abstract

This paper introduces a second-order differentiability smoothing technique to the classical l 1 exact penalty function for constrained optimization problems(COP). Error estimations among the optimal objective values of the nonsmooth penalty problem, the smoothed penalty problem and the original optimization problem are obtained. Based on the smoothed problem, an algorithm for solving COP is proposed and some preliminary numerical results indicate that the algorithm is quite promising. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Xinsheng Xu & Zhiqing Meng & Jianwu Sun & Liguo Huang & Rui Shen, 2013. "A second-order smooth penalty function algorithm for constrained optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 155-172, May.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:1:p:155-172
    DOI: 10.1007/s10589-012-9504-9
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    References listed on IDEAS

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    1. Israel Zang, 1981. "Discontinuous Optimization by Smoothing," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 140-152, February.
    2. X. X. Huang & X. Q. Yang, 2001. "Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 615-640, December.
    3. Lasserre, J. B., 1981. "A globally convergent algorithm for exact penalty functions," European Journal of Operational Research, Elsevier, vol. 7(4), pages 389-395, August.
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    Cited by:

    1. Duan Yaqiong & Lian Shujun, 2016. "Smoothing Approximation to the Square-Root Exact Penalty Function," Journal of Systems Science and Information, De Gruyter, vol. 4(1), pages 87-96, February.

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