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Invex Functions and Generalized Convexity in Multiobjective Programming

Author

Listed:
  • R. Osuna-Gómez

    (Universidad de Sevilla)

  • A. Rufián-Lizana

    (Universidad de Sevilla)

  • P. Ruíz-Canales

    (Universidad de Sevilla)

Abstract

Martin (Ref. 1) studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Kuhn–Tucker points (depending on the case) remains true if we optimize several objective functions instead of one objective function. To this end, we define accurately stationary points and Kuhn–Tucker optimality conditions for multiobjective programming problems. We see that the Martin results cannot be improved in mathematical programming, because the new types of generalized convexity that have appeared over the last few years do not yield any new optimality conditions for mathematical programming problems.

Suggested Citation

  • R. Osuna-Gómez & A. Rufián-Lizana & P. Ruíz-Canales, 1998. "Invex Functions and Generalized Convexity in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 651-661, September.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:3:d:10.1023_a:1022628130448
    DOI: 10.1023/A:1022628130448
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    Cited by:

    1. Manuel Arana-Jiménez & Riccardo Cambini & Laura Carosi, 2018. "A reduced formulation for pseudoinvex vector functions," Annals of Operations Research, Springer, vol. 269(1), pages 21-27, October.
    2. Balendu Bhooshan Upadhyay & Arnav Ghosh & Savin Treanţă, 2024. "Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 89(3), pages 723-744, July.
    3. Tadeusz Antczak, 2022. "Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints," 4OR, Springer, vol. 20(3), pages 417-442, September.
    4. Vsevolod Ivanov, 2011. "Second-order Kuhn-Tucker invex constrained problems," Journal of Global Optimization, Springer, vol. 50(3), pages 519-529, July.

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