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

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, ETSII, Edificio de Tecnologías de la Información y las Telecomunicaciones, Universidad de Valladolid, Campus Miguel Delibes, s/n, 47011, Valladolid, Spain

    César Gutiérrez

  2. Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca, Campus Miguel de Unamuno, s/n, 37007, Salamanca, Spain

    Bienvenido Jiménez

  3. Departamento de Matemática Aplicada, ETSII, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal, 12, 28040, Madrid, Spain

    Vicente Novo

Authors
  1. César Gutiérrez
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  2. Bienvenido Jiménez
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  3. Vicente Novo
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Correspondence to César Gutiérrez.

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Gutiérrez, C., Jiménez, B. & Novo, V. Multiplier Rules and Saddle-Point Theorems for Helbig’s Approximate Solutions in Convex Pareto Problems. J Glob Optim 32, 367–383 (2005). https://doi.org/10.1007/s10898-004-5904-4

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  • DOI: https://doi.org/10.1007/s10898-004-5904-4

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