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Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results

Author

Listed:
  • Giorgio Giorgi

    (University of Pavia)

  • Bienvenido Jiménez

    (E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED))

  • Vicente Novo

    (E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED))

Abstract

An overview is given on the use of Dini and Hadamard directional derivatives in various types of multiobjective optimization problems. Necessary optimality conditions are considered for a problem with an abstract constraint, for a problem with inequality and equality constraints and for a problem with both inequality and equality constraints and an abstract constraint. The issue of constraint qualifications is examined, and several first-order sufficient optimality conditions are presented for the third type of multiobjective optimization problems.

Suggested Citation

  • Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2023. "Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(2), pages 355-377, December.
  • Handle: RePEc:spr:decfin:v:46:y:2023:i:2:d:10.1007_s10203-023-00403-3
    DOI: 10.1007/s10203-023-00403-3
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    References listed on IDEAS

    as
    1. B. Jiménez & V. Novo, 2006. "Characterization of the Cone of Attainable Directions," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 493-499, December.
    2. G. Giorgi & S. Komlósi, 1992. "Dini derivatives in optimization — Part I," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 15(1), pages 3-30, March.
    3. X. F. Li, 2000. "Constraint Qualifications in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 373-398, August.
    4. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    5. V. Preda & I. Chiţescu, 1999. "On Constraint Qualification in Multiobjective Optimization Problems: Semidifferentiable Case," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 417-433, February.
    6. X. F. Li & J. Z. Zhang, 2005. "Stronger Kuhn-Tucker Type Conditions in Nonsmooth Multiobjective Optimization: Locally Lipschitz Case," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 367-388, November.
    7. Regina S. Burachik & M. M. Rizvi, 2012. "On Weak and Strong Kuhn–Tucker Conditions for Smooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 477-491, November.
    8. G. Giorgi & B. Jiménez & V. Novo, 2009. "Strong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 288-304, December.
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    10. G. Giorgi & S. Komlósi, 1992. "Dini derivatives in optimization — Part II," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 15(2), pages 3-24, September.
    11. Giorgio Giorgi & Sándor Komlósi, 1995. "Dini derivatives in optimization — Part III," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 18(1), pages 47-63, March.
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    More about this item

    Keywords

    Multiobjective optimization problems; Dini derivatives; Hadamard derivatives; Optimality conditions; Constraint qualifications;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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