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A penalty-free method with superlinear convergence for equality constrained optimization

Author

Listed:
  • Zhongwen Chen

    (Soochow University)

  • Yu-Hong Dai

    (Chinese Academy of Sciences)

  • Jiangyan Liu

    (Soochow University)

Abstract

In this paper, we propose a new penalty-free method for solving nonlinear equality constrained optimization. This method uses different trust regions to cope with the nonlinearity of the objective function and the constraints instead of using a penalty function or a filter. To avoid Maratos effect, we do not make use of the second order correction or the nonmonotone technique, but utilize the value of the Lagrangian function instead of the objective function in the acceptance criterion of the trial step. The feasibility restoration phase is not necessary, which is often used in filter methods or some other penalty-free methods. Global and superlinear convergence are established for the method under standard assumptions. Preliminary numerical results are reported, which demonstrate the usefulness of the proposed method.

Suggested Citation

  • Zhongwen Chen & Yu-Hong Dai & Jiangyan Liu, 2020. "A penalty-free method with superlinear convergence for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 801-833, July.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:3:d:10.1007_s10589-019-00117-6
    DOI: 10.1007/s10589-019-00117-6
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    References listed on IDEAS

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    1. Chungen Shen & Sven Leyffer & Roger Fletcher, 2012. "A nonmonotone filter method for nonlinear optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 583-607, July.
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    Cited by:

    1. Yonggang Pei & Shaofang Song & Detong Zhu, 2023. "A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization," Computational Optimization and Applications, Springer, vol. 84(3), pages 1005-1033, April.
    2. Ernesto G. Birgin, 2020. "Preface of the special issue dedicated to the XII Brazilian workshop on continuous optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 615-619, July.

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