IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v156y2013i2d10.1007_s10957-012-0114-6.html
   My bibliography  Save this article

A Gauss–Newton Approach for Solving Constrained Optimization Problems Using Differentiable Exact Penalties

Author

Listed:
  • Roberto Andreani

    (State University of Campinas)

  • Ellen H. Fukuda

    (State University of Campinas)

  • Paulo J. S. Silva

    (University of São Paulo)

Abstract

We propose a Gauss–Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by André and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of the KKT conditions as a system of equations. Such reformulation allows the use of a semismooth Newton method, so that local superlinear convergence rate can be proved under an assumption weaker than the usual strong second-order sufficient condition and without requiring strict complementarity. Besides, we note that the exact penalty function can be used to globalize the method. We conclude with some numerical experiments using the collection of test problems CUTE.

Suggested Citation

  • Roberto Andreani & Ellen H. Fukuda & Paulo J. S. Silva, 2013. "A Gauss–Newton Approach for Solving Constrained Optimization Problems Using Differentiable Exact Penalties," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 417-449, February.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0114-6
    DOI: 10.1007/s10957-012-0114-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0114-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-0114-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    2. Thiago André & Paulo Silva, 2010. "Exact penalties for variational inequalities with applications to nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 47(3), pages 401-429, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ellen H. Fukuda & Bruno F. Lourenço, 2018. "Exact augmented Lagrangian functions for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 71(2), pages 457-482, November.
    2. Ng, Kenyon & Turlach, Berwin A. & Murray, Kevin, 2019. "A flexible sequential Monte Carlo algorithm for parametric constrained regression," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 13-26.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kaiwen Meng & Xiaoqi Yang, 2015. "First- and Second-Order Necessary Conditions Via Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 720-752, June.
    2. M. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 728-744, March.
    3. Antczak, Tadeusz, 2009. "Exact penalty functions method for mathematical programming problems involving invex functions," European Journal of Operational Research, Elsevier, vol. 198(1), pages 29-36, October.
    4. Tiago Andrade & Nikita Belyak & Andrew Eberhard & Silvio Hamacher & Fabricio Oliveira, 2022. "The p-Lagrangian relaxation for separable nonconvex MIQCQP problems," Journal of Global Optimization, Springer, vol. 84(1), pages 43-76, September.
    5. Pan, Yan & Duan, Fabing & Xu, Liyan & Chapeau-Blondeau, François, 2019. "Benefits of noise in M-estimators: Optimal noise level and probability density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    6. A. J. Zaslavski, 2014. "An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 649-664, August.
    7. T. Antczak, 2018. "Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 205-224, January.
    8. Ellen H. Fukuda & L. M. Graña Drummond & Fernanda M. P. Raupp, 2016. "An external penalty-type method for multicriteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 493-513, July.
    9. D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
    10. Duan Yaqiong & Lian Shujun, 2016. "Smoothing Approximation to the Square-Root Exact Penalty Function," Journal of Systems Science and Information, De Gruyter, vol. 4(1), pages 87-96, February.
    11. T. Antczak, 2013. "A Lower Bound for the Penalty Parameter in the Exact Minimax Penalty Function Method for Solving Nondifferentiable Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 437-453, November.
    12. Rao, K.S. Rama & Sunderan, T. & Adiris, M. Ref'at, 2017. "Performance and design optimization of two model based wave energy permanent magnet linear generators," Renewable Energy, Elsevier, vol. 101(C), pages 196-203.
    13. Tadeusz Antczak & Najeeb Abdulaleem, 2023. "On the exactness and the convergence of the $$l_{1}$$ l 1 exact penalty E-function method for E-differentiable optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1331-1359, September.
    14. Marco Corazza & Giovanni Fasano & Riccardo Gusso, 2011. "Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem," Working Papers 2011_10, Department of Economics, University of Venice "Ca' Foscari".
    15. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2014. "Some Notes on Approximate Optimality Conditions in Scalar and Vector Optimization Problems," DEM Working Papers Series 095, University of Pavia, Department of Economics and Management.
    16. X. Q. Yang & Y. Y. Zhou, 2010. "Second-Order Analysis of Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 445-461, August.
    17. Amaioua, Nadir & Audet, Charles & Conn, Andrew R. & Le Digabel, Sébastien, 2018. "Efficient solution of quadratically constrained quadratic subproblems within the mesh adaptive direct search algorithm," European Journal of Operational Research, Elsevier, vol. 268(1), pages 13-24.
    18. Marco Corazza & Stefania Funari & Riccardo Gusso, 2012. "An evolutionary approach to preference disaggregation in a MURAME-based credit scoring problem," Working Papers 5, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    19. Xinhua Mao & Jianwei Wang & Changwei Yuan & Wei Yu & Jiahua Gan, 2018. "A Dynamic Traffic Assignment Model for the Sustainability of Pavement Performance," Sustainability, MDPI, vol. 11(1), pages 1-19, December.
    20. Ellen H. Fukuda & Bruno F. Lourenço, 2018. "Exact augmented Lagrangian functions for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 71(2), pages 457-482, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0114-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.