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Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency

Author

Listed:
  • Naoki Hamada

    (KLab Inc.
    The RIKEN Center for Advanced Intelligence Project)

  • Shunsuke Ichiki

    (Tokyo Institute of Technology)

Abstract

In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what condition ensures that all weakly efficient solutions are efficient. In this paper, we give a condition to verify when efficiency coincides with weak efficiency, provided that the free disposal hull of a given set is convex. By using this characterization, we obtain various applications to multi-objective optimization problems under some convex conditions. We also apply the main theorem to the least absolute shrinkage and selection operator (LASSO) and show that for a multi-objective version of LASSO, all weakly efficient solutions are efficient. Numerical simulation demonstrates that this equivalence is helpful to accelerate the hyper-parameter search for LASSO.

Suggested Citation

  • Naoki Hamada & Shunsuke Ichiki, 2022. "Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 248-270, January.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01961-5
    DOI: 10.1007/s10957-021-01961-5
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. James Ward, 1989. "Structure of Efficient Sets for Convex Objectives," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 249-257, May.
    3. T. J. Lowe & J.-F. Thisse & J. E. Ward & R. E. Wendell, 1984. "On Efficient Solutions to Multiple Objective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1346-1349, November.
    4. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    5. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    6. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    7. Matthias Ehrgott & Stefan Nickel, 2002. "On the number of criteria needed to decide Pareto optimality," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 329-345, June.
    8. Matthias Ehrgott & Stefan Nickel, 2002. "On the number of criteria needed to decide Pareto optimality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 329-345, June.
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