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Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization

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Abstract

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.

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Notes

  1. Liang et al. [35].

  2. Birgin et al. [37].

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Acknowledgements

The authors would like to thank the referees, the Associate Editor and the Editor-in-Chief 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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Authors and Affiliations

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

    M. Fernanda P. Costa

  2. Center for Research and Innovation in Business Sciences and Information Systems, Polytechnic of Porto, Porto, Portugal

    Rogério B. Francisco

  3. Algoritmi Research Centre, University of Minho, 4710-057, Braga, Portugal

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

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  1. M. Fernanda P. Costa
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  2. Rogério B. Francisco
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  3. Ana Maria A. C. Rocha
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  4. Edite M. G. P. Fernandes
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Correspondence to M. Fernanda P. Costa.

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Costa, M.F.P., Francisco, R.B., Rocha, A.M.A.C. et al. Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization. J Optim Theory Appl 174, 875–893 (2017). https://doi.org/10.1007/s10957-016-1042-7

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