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Newton’s method may fail to recognize proximity to optimal points in constrained optimization

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Abstract

We will show examples in which the primal sequence generated by the Newton–Lagrange method converges to a strict local minimizer of a constrained optimization problem but the gradient of the Lagrangian does not tend to zero, independently of the choice of the dual sequence.

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Acknowledgments

We wish to acknowledge the associate editor and two anonymous referees for insightful comments that helped us a lot to improve this paper. This work was kindly supported by the Brazilian research agencies CNPq (303013/2013–3, 305078/2013–5), PRONEX-CNPq/FAPERJ (E–26/111.449/2010–APQ1), and FAPESP (2010/10133–0, 2013/05475–7, 2013/07375–0).

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Authors and Affiliations

  1. DMA/IMECC, University of Campinas – UNICAMP, Campinas, SP, Brazil

    R. Andreani, J. M. Martínez & L. T. Santos

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  1. R. Andreani
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  2. J. M. Martínez
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  3. L. T. Santos
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Correspondence to L. T. Santos.

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Andreani, R., Martínez, J.M. & Santos, L.T. Newton’s method may fail to recognize proximity to optimal points in constrained optimization. Math. Program. 160, 547–555 (2016). https://doi.org/10.1007/s10107-016-0994-6

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  • DOI: https://doi.org/10.1007/s10107-016-0994-6

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