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Congress of APDIO, the Portuguese Operational Research Society

APDIO 2017: Operational Research pp 39–55Cite as

A Penalty Approach for Solving Nonsmooth and Nonconvex MINLP Problems

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 223)

Abstract

This paper presents a penalty approach for globally solving nonsmooth and nonconvex mixed-integer nonlinear programming (MINLP) problems. Both integrality constraints and general nonlinear constraints are handled separately by hyperbolic tangent penalty functions. Proximity from an iterate to a feasible promising solution is enforced by an oracle penalty term. The numerical experiments show that the proposed oracle-based penalty approach is effective in reaching the solutions of the MINLP problems and is competitive when compared with other strategies.

Keywords

  • MINLP
  • Penalty function
  • DIRECT
  • Oracle

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Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments and suggestions to improve the paper.

This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundação para a Ciência e Tecnologia, within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.

Author information

Authors and Affiliations

  1. Centre of Mathematics, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    M. Fernanda P. Costa

  2. Algoritmi Research Centre, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha & Edite M. G. P. Fernandes

Authors
  1. M. Fernanda P. Costa
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  2. Ana Maria A. C. Rocha
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  3. Edite M. G. P. Fernandes
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Corresponding author

Correspondence to M. Fernanda P. Costa .

Editor information

Editors and Affiliations

  1. School of Engineering, University of Minho, School of Engineering, Braga, Portugal

    Prof. Dr. A. Ismael F. Vaz

  2. Department of Mathematics and LIAAD-INESC TEC, Polytechnic Institute of Bragança, School of Technology and Management, Bragança, Portugal

    Prof. Dr. João Paulo Almeida

  3. INESC TEC - Faculty of Engineering, University of Porto, INESC TEC - Faculty of Engineering, Porto, Portugal

    Prof. Dr. José Fernando Oliveira

  4. Department of Mathematics, University of Porto, Department of Mathematics, Porto, Portugal

    Prof. Dr. Alberto Adrego Pinto

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Cite this paper

Costa, M.F.P., Rocha, A.M.A.C., Fernandes, E.M.G.P. (2018). A Penalty Approach for Solving Nonsmooth and Nonconvex MINLP Problems. In: Vaz, A., Almeida, J., Oliveira, J., Pinto, A. (eds) Operational Research. APDIO 2017. Springer Proceedings in Mathematics & Statistics, vol 223. Springer, Cham. https://doi.org/10.1007/978-3-319-71583-4_4

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