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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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    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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