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An external penalty-type method for multicriteria

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Abstract

We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method uses an auxiliary function, which can be chosen among large classes of “monotonic” real-valued mappings. We analyze the properties of the auxiliary functions in those classes and exhibit some examples. The convergence results are similar to those of the scalar-valued method, and depending on the kind of auxiliary function used in the implementation, under standard assumptions, the generated infeasible sequences converge to weak Pareto or Pareto optimal points. We also propose an implementable local version of the external penalization method and study its convergence results.

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Acknowledgments

We would like to thank the anonymous referees for their suggestions which improved the original version of the paper. We are also thankful to Alfredo N. Iusem and Benar F. Svaiter for valuable discussions.

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Ellen H. Fukuda

  2. Faculty of Business and Administration, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, 22290-240, Brazil

    L. M. Graña Drummond

  3. National Laboratory for Scientific Computing, Petrópolis, RJ, 25651-075, Brazil

    Fernanda M. P. Raupp

Authors
  1. Ellen H. Fukuda
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  2. L. M. Graña Drummond
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  3. Fernanda M. P. Raupp
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Corresponding author

Correspondence to Ellen H. Fukuda.

Additional information

This work was supported by Grant-in-Aid for Young Scientists (B) (26730012) from Japan Society for the Promotion of Science and a Grant (311165/2013-3) from National Counsel of Technological and Scientific Development (CNPq).

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Fukuda, E.H., Drummond, L.M.G. & Raupp, F.M.P. An external penalty-type method for multicriteria. TOP 24, 493–513 (2016). https://doi.org/10.1007/s11750-015-0406-8

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  • DOI: https://doi.org/10.1007/s11750-015-0406-8

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