A Penalty Approach for Solving Nonsmooth and Nonconvex MINLP Problems

  • M. Fernanda P. Costa
  • Ana Maria A. C. Rocha
  • Edite M. G. P. Fernandes
Conference paper
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 

Notes

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.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • M. Fernanda P. Costa
    • 1
  • Ana Maria A. C. Rocha
    • 2
  • Edite M. G. P. Fernandes
    • 2
  1. 1.Centre of MathematicsUniversity of Minho, Campus de GualtarBragaPortugal
  2. 2.Algoritmi Research CentreUniversity of Minho, Campus de GualtarBragaPortugal

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