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

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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.

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Authors and Affiliations

  1. School of Mathematical Science, Soochow University, Suzhou, 215006, People’s Republic of China

    Zhongwen Chen & Jiangyan Liu

  2. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yu-Hong Dai

Authors
  1. Zhongwen Chen
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  2. Yu-Hong Dai
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  3. Jiangyan Liu
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Correspondence to Yu-Hong Dai.

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Z. Chen: His work was supported by the Chinese NSF Grant (No. 11871362). Y. Dai: His work was supported by the Key Projects of the Chinese NSF Grant (No. 11631013), the National Funds for Distinguished Young Scientists (No. 11125107) and the National 973 Program of China (No. 2015CB856002).

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Chen, Z., Dai, YH. & Liu, J. A penalty-free method with superlinear convergence for equality constrained optimization. Comput Optim Appl 76, 801–833 (2020). https://doi.org/10.1007/s10589-019-00117-6

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  • DOI: https://doi.org/10.1007/s10589-019-00117-6

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