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A primal–dual augmented Lagrangian penalty-interior-point filter line search algorithm

Author

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  • Renke Kuhlmann

    (University of Bremen)

  • Christof Büskens

    (University of Bremen)

Abstract

Interior-point methods have been shown to be very efficient for large-scale nonlinear programming. The combination with penalty methods increases their robustness due to the regularization of the constraints caused by the penalty term. In this paper a primal–dual penalty-interior-point algorithm is proposed, that is based on an augmented Lagrangian approach with an $$\ell 2$$ ℓ 2 -exact penalty function. Global convergence is maintained by a combination of a merit function and a filter approach. Unlike the majority of filter methods, no separate feasibility restoration phase is required. The algorithm has been implemented within the solver WORHP to study different penalty and line search options and to compare its numerical performance to two other state-of-the-art nonlinear programming algorithms, the interior-point method IPOPT and the sequential quadratic programming method of WORHP.

Suggested Citation

  • Renke Kuhlmann & Christof Büskens, 2018. "A primal–dual augmented Lagrangian penalty-interior-point filter line search algorithm," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 451-483, June.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:3:d:10.1007_s00186-017-0625-x
    DOI: 10.1007/s00186-017-0625-x
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    References listed on IDEAS

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    1. Paul Armand & Joël Benoist & Riadh Omheni & Vincent Pateloup, 2014. "Study of a primal-dual algorithm for equality constrained minimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 405-433, December.
    2. Chungen Shen & Lei-Hong Zhang & Wei Liu, 2016. "A stabilized filter SQP algorithm for nonlinear programming," Journal of Global Optimization, Springer, vol. 65(4), pages 677-708, August.
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    Cited by:

    1. Renke Kuhlmann, 2019. "Learning to steer nonlinear interior-point methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 381-419, December.

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