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Quasi-Newton methods for constrained nonlinear systems: complexity analysis and applications

Author

Listed:
  • Leopoldo Marini

    (Università di Firenze)

  • Benedetta Morini

    (Università di Firenze)

  • Margherita Porcelli

    (Università di Firenze)

Abstract

We address the solution of constrained nonlinear systems by new linesearch quasi-Newton methods. These methods are based on a proper use of the projection map onto the convex constraint set and on a derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of the proposed scheme are discussed and validated on bound-constrained problems including gas distribution network models. The results reported show that the new methods are very efficient and competitive with an existing affine-scaling procedure.

Suggested Citation

  • Leopoldo Marini & Benedetta Morini & Margherita Porcelli, 2018. "Quasi-Newton methods for constrained nonlinear systems: complexity analysis and applications," Computational Optimization and Applications, Springer, vol. 71(1), pages 147-170, September.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-018-9980-7
    DOI: 10.1007/s10589-018-9980-7
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    References listed on IDEAS

    as
    1. Carcasci, C. & Marini, L. & Morini, B. & Porcelli, M., 2016. "A new modular procedure for industrial plant simulations and its reliable implementation," Energy, Elsevier, vol. 94(C), pages 380-390.
    2. Lijuan Zhao & Wenyu Sun, 2013. "A Conic Affine Scaling Dogleg Method For Nonlinear Optimization With Bound Constraints," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-30.
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    Cited by:

    1. Wei Ouyang & Kui Mei, 2023. "A General Iterative Procedure for Solving Nonsmooth Constrained Generalized Equations," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
    2. Valeria Ruggiero & Gerardo Toraldo, 2018. "Introduction to the special issue for SIMAI 2016," Computational Optimization and Applications, Springer, vol. 71(1), pages 1-3, September.
    3. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    4. Jiaxi Wang & Wei Ouyang, 2022. "Newton’s Method for Solving Generalized Equations Without Lipschitz Condition," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 510-532, February.

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