Journal of Optimization Theory and Applications

, Volume 98, Issue 3, pp 651–661 | Cite as

Invex Functions and Generalized Convexity in Multiobjective Programming

  • R. Osuna-Gómez
  • A. Rufián-Lizana
  • P. Ruíz-Canales


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.

Invex functions KT-invex problems Kuhn–Tucker optimality conditions weakly efficient points 


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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • R. Osuna-Gómez
    • 1
  • A. Rufián-Lizana
    • 1
  • P. Ruíz-Canales
    • 1
  1. 1.Departamento de Estadística e Investigación Operativa, Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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