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Outer Trust-Region Method for Constrained Optimization

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Abstract

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an outer trust-region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones, and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the “greediness phenomenon” of nonlinear programming. Convergence results for an OTR version of an augmented Lagrangian method for nonconvex constrained optimization are proved, and numerical experiments are presented.

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Authors and Affiliations

  1. Department of Computer Science IME-USP, University of São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil

    Ernesto G. Birgin

  2. 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

Authors
  1. Ernesto G. Birgin
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  2. Emerson V. Castelani
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  3. André L. M. Martinez
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  4. J. M. Martínez
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Corresponding author

Correspondence to Ernesto G. Birgin.

Additional information

Communicated by Liqun Qi.

This work was supported by PRONEX-CNPq/FAPERJ (E-26/111.449/2010-APQ1), FAPESP (Grants 2006/53768-0 and 2005/57684-2), and CNPq.

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Birgin, E.G., Castelani, E.V., Martinez, A.L.M. et al. Outer Trust-Region Method for Constrained Optimization. J Optim Theory Appl 150, 142–155 (2011). https://doi.org/10.1007/s10957-011-9815-5

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  • DOI: https://doi.org/10.1007/s10957-011-9815-5

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