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Smoothing Approximation to the New Exact Penalty Function with Two Parameters

Author

Listed:
  • Jing Qiu

    (School of Mathematical Science, Qufu Normal University, Qufu, Shandong 273165, P. R. China)

  • Jiguo Yu

    (School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong 250353, P. R. China3Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan, Shandong 250014, P. R. China4Shandong Laboratory of Computer Networks, Jinan 250014, P. R. China)

  • Shujun Lian

    (School of Management, Qufu Normal University, Rizhao, Shandong Province, P. R. China)

Abstract

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

Suggested Citation

  • Jing Qiu & Jiguo Yu & Shujun Lian, 2021. "Smoothing Approximation to the New Exact Penalty Function with Two Parameters," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-19, October.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400108
    DOI: 10.1142/S0217595921400108
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