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On the Fritz John saddle point problem for differentiable multiobjective optimization

Author

Listed:
  • Maria C. Maciel

    (Universidad Nacional del Sur)

  • Sandra A. Santos

    (Universidade Estadual de Campinas)

  • Graciela N. Sottosanto

    (Universidad Nacional del Comahue (AR))

Abstract

In this contribution, the relationship between saddle points of Lagrangian functions associated with the inequality constrained multiobjective optimization problem and Fritz John critical points are presented under generalized notions of convexity. Assuming invexity and an extended Slater-type condition upon the multiobjective problem, a regular solution to the Fritz-John system is obtained that encompasses all the objective functions. Also, a new class of generalized convex problems is defined, and its connections with other existing classes are established.

Suggested Citation

  • Maria C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2016. "On the Fritz John saddle point problem for differentiable multiobjective optimization," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 917-933, December.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:4:d:10.1007_s12597-016-0253-x
    DOI: 10.1007/s12597-016-0253-x
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    References listed on IDEAS

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    1. J. B. G. Frenk & G. Kassay, 1999. "On Classes of Generalized Convex Functions, Gordan–Farkas Type Theorems, and Lagrangian Duality," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 315-343, August.
    2. M. C. Maciel & S. A. Santos & G. N. Sottosanto, 2009. "Regularity Conditions in Differentiable Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 385-398, August.
    3. Majid Soleimani-Damaneh, 2015. "Generalized Convexity and Characterization of (Weak) Pareto-Optimality in Nonsmooth Multiobjective Optimization Problems," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 877-899.
    4. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2011. "On Second-Order Optimality Conditions for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 332-351, May.
    5. G. Bigi & M. Pappalardo, 1999. "Regularity Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 83-96, July.
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