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Constrained derivative-free optimization on thin domains

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Abstract

Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function f is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented.

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Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil

    J. M. Martínez & F. N. C. Sobral

Authors
  1. J. M. Martínez
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  2. F. N. C. Sobral
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Correspondence to F. N. C. Sobral.

Additional information

This work was supported by PRONEX-CNPq/FAPERJ Grant E-26/171.164/2003-APQ1, FAPESP Grants 03/09169-6, 06/53768-0 and 08/00468-4, and CNPq.

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Martínez, J.M., Sobral, F.N.C. Constrained derivative-free optimization on thin domains. J Glob Optim 56, 1217–1232 (2013). https://doi.org/10.1007/s10898-012-9944-x

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