Journal of Global Optimization

, Volume 32, Issue 3, pp 367–383 | Cite as

Multiplier Rules and Saddle-Point Theorems for Helbig’s Approximate Solutions in Convex Pareto Problems

  • César GutiérrezEmail author
  • Bienvenido Jiménez
  • Vicente Novo


This paper deals with approximate Pareto solutions in convex multiobjective optimization problems. We relate two approximate Pareto efficiency concepts: one is already classic and the other is due to Helbig. We obtain Fritz John and Kuhn–Tucker type necessary and sufficient conditions for Helbig’s approximate solutions. An application we deduce saddle-point theorems corresponding to these solutions for two vector-valued Lagrangian functions.


Approximate solutions Lagrangian functions ε-Pareto optimality ε-Saddle-points ε-Subdifferential 

Mathematics Subject Classifications

90C29 49M37 


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Copyright information

© Springer 2005

Authors and Affiliations

  • César Gutiérrez
    • 1
    Email author
  • Bienvenido Jiménez
    • 2
  • Vicente Novo
    • 3
  1. 1.Departamento de Matemática Aplicada, ETSII, Edificio de Tecnologías de la Información y las TelecomunicacionesUniversidad de ValladolidValladolidSpain
  2. 2.Departamento de Economía e Historia Económica, Facultad de Economía y EmpresaUniversidad de SalamancaSalamancaSpain
  3. 3.Departamento de Matemática Aplicada, ETSIIUniversidad Nacional de Educación a DistanciaMadridSpain

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