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Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians

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Abstract

When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill-conditioning harms the overall convergence. In this paper a regularization approach is suggested to overcome this difficulty. An Augmented Lagrangian method is defined with the addition of a regularization term that inhibits the possibility that the iterates go far from a reference point. Convergence proofs and numerical examples are given.

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Authors and Affiliations

  1. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970, Campinas, SP, Brazil

    Emerson V. Castelani, André L. M. Martinez & J. M. Martínez

  2. Institute of Pure and Applied Mathematics (IMPA), Rio de Janeiro, Brazil

    B. F. Svaiter

Authors
  1. Emerson V. Castelani
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  2. André L. M. Martinez
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  3. J. M. Martínez
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  4. B. F. Svaiter
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Corresponding author

Correspondence to Emerson V. Castelani.

Additional information

E.V. Castelani was supported by PRONEX-Optimization (PRONEX—CNPq/FAPERJ E-26/171.164/2003—APQ1), FAPESP (Grants 06/53768-0 and 05-56773-1) and CNPq.

A.L.M. Martinez was supported by PRONEX-Optimization (PRONEX—CNPq/FAPERJ E-26/171.164/2003—APQ1), FAPESP (Grants 06/53768-0 and 05-56773-1) and CAPES.

J.M. Martínez was supported by PRONEX-Optimization (PRONEX—CNPq/FAPERJ E-26/171.164/2003—APQ1), FAPESP (Grant 06/53768-0) and CNPq.

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Castelani, E.V., Martinez, A.L.M., Martínez, J.M. et al. Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians. Comput Optim Appl 46, 229–245 (2010). https://doi.org/10.1007/s10589-009-9271-4

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  • DOI: https://doi.org/10.1007/s10589-009-9271-4

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