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On the convergence of a smoothed penalty algorithm for semi-infinite programming

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Listed:
  • Qian Liu
  • Changyu Wang
  • Xinmin Yang

Abstract

For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact $$l_\rho (0>\rho \le 1)$$ penalty functions. On base of the smoothed penalty function, we present a feasible penalty algorithm for solving SIP. Without any boundedness condition or coercive condition, we establish the global convergence theorem. Then we present a perturbation theorem for this algorithm and obtain a necessary and sufficient condition for the convergence to the optimal value of SIP. Under Mangasarian–Fromovitz constrained qualification condition, we further discuss the convergence properties for the algorithm based upon a subclass of smooth approximations to the exact $$l_\rho $$ penalty function. Finally, numerical results are given. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Qian Liu & Changyu Wang & Xinmin Yang, 2013. "On the convergence of a smoothed penalty algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 203-220, October.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:2:p:203-220
    DOI: 10.1007/s00186-013-0440-y
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    References listed on IDEAS

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    1. C. Ling & L. Q. Qi & G. L. Zhou & S. Y. Wu, 2006. "Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 147-164, April.
    2. Dong-Hui Li & Liqun Qi & Judy Tam & Soon-Yi Wu, 2004. "A Smoothing Newton Method for Semi-Infinite Programming," Journal of Global Optimization, Springer, vol. 30(2), pages 169-194, November.
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    Cited by:

    1. Jiachen Ju & Qian Liu, 2020. "Convergence properties of a class of exact penalty methods for semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 383-403, June.

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