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An external penalty-type method for multicriteria

Author

Listed:
  • Ellen H. Fukuda

    (Kyoto University)

  • L. M. Graña Drummond

    (Federal University of Rio de Janeiro)

  • Fernanda M. P. Raupp

    (National Laboratory for Scientific Computing)

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.

Suggested Citation

  • Ellen H. Fukuda & L. M. Graña Drummond & Fernanda M. P. Raupp, 2016. "An external penalty-type method for multicriteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 493-513, July.
    • Handle: RePEc:spr:topjnl:v:24:y:2016:i:2:d:10.1007_s11750-015-0406-8
    DOI: 10.1007/s11750-015-0406-8
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    References listed on IDEAS

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    1. Leschine, Thomas M. & Wallenius, Hannele & Verdini, William A., 1992. "Interactive multiobjective analysis and assimilative capacity-based ocean disposal decisions," European Journal of Operational Research, Elsevier, vol. 56(2), pages 278-289, January.
    2. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    3. Yan Fu & Urmila Diwekar, 2004. "An Efficient Sampling Approach to Multiobjective Optimization," Annals of Operations Research, Springer, vol. 132(1), pages 109-134, November.
    4. Gravel, Marc & Martel, Jean Marc & Nadeau, Raymond & Price, Wilson & Tremblay, Richard, 1992. "A multicriterion view of optimal resource allocation in job-shop production," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 230-244, August.
    5. White, D.J., 1998. "Epsilon-dominating solutions in mean-variance portfolio analysis," European Journal of Operational Research, Elsevier, vol. 105(3), pages 457-466, March.
    6. E. Carrizosa & J. B. G. Frenk, 1998. "Dominating Sets for Convex Functions with Some Applications," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 281-295, February.
    7. Ellen Fukuda & L. Graña Drummond, 2013. "Inexact projected gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 473-493, April.
    8. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
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    Cited by:

    1. Bosch, Jonathan & Staffell, Iain & Hawkes, Adam D., 2018. "Temporally explicit and spatially resolved global offshore wind energy potentials," Energy, Elsevier, vol. 163(C), pages 766-781.

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