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A derivative-free trust-funnel method for equality-constrained nonlinear optimization

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Abstract

A new derivative-free method is proposed for solving equality-constrained nonlinear optimization problems. This method is of the trust-funnel variety and is also based on the use of polynomial interpolation models. In addition, it uses a self-correcting geometry procedure in order to ensure that the interpolation problem is well defined in the sense that the geometry of the set of interpolation points does not differ too much from the ideal one. The algorithm is described in detail and some encouraging numerical results are presented.

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Acknowledgments

The first author gratefully acknowledges a CERUNA-UNamur scholarship.

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Authors and Affiliations

  1. Namur Center for Complex Systems (naXys) and Department of Mathematics, University of Namur, 61, rue de Bruxelles, 5000, Namur, Belgium

    Ph. R. Sampaio & Ph. L. Toint

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  1. Ph. R. Sampaio
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  2. Ph. L. Toint
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Correspondence to Ph. R. Sampaio.

Appendix

Appendix

See the Table 1, 2

Table 1 Number of function evaluations required by DEFT-FUNNEL, CDFO and COBYLA methods to converge in the first type of comparison
Full size table
Table 2 Number of function evaluations required by DEFT-FUNNEL, CDFO and COBYLA methods to converge in the second type of comparison
Full size table

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Sampaio, P.R., Toint, P.L. A derivative-free trust-funnel method for equality-constrained nonlinear optimization. Comput Optim Appl 61, 25–49 (2015). https://doi.org/10.1007/s10589-014-9715-3

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