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Smoothing Approximation to the Square-Root Exact Penalty Function

Author

Listed:
  • Duan Yaqiong

    (College of Management, Qufu Normal University, Rizhao276826, China)

  • Lian Shujun

    (College of Management, Qufu Normal University, Rizhao276826, China)

Abstract

In this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jossai:v:4:y:2016:i:1:p:87-96:n:6
    DOI: 10.1515/JSSI-2016-0087
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    References listed on IDEAS

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    1. X.X. Huang & X.Q. Yang, 2003. "Convergence Analysis of a Class of Nonlinear Penalization Methods for Constrained Optimization via First-Order Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 311-332, February.
    2. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    3. X. L. Sun & D. Li, 1999. "Value-Estimation Function Method for Constrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 385-409, August.
    4. 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.
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