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

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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