Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones

• C. Gutiérrez ^[1] ; L. Huerga ^[2] ; B. Jiménez ^[2] ; V. Novo ^[2]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
  2. [2] Universidad Nacional de Educación a Distancia

     Universidad Nacional de Educación a Distancia

     Madrid, España

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 28, Nº. 2, 2020, págs. 526-544
• Idioma: inglés
• DOI: 10.1007/s11750-020-00546-1
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• Resumen

  • In this paper, we provide optimality conditions for approximate proper solutions of a multiobjective optimization problem, whose feasible set is given by a cone constraint and the ordering cone is polyhedral. A first class of optimality conditions is given by means of a nonlinear scalar Lagrangian and the second kind through a linear scalarization technique, under generalized convexity hypotheses, that lets us derive a Kuhn–Tucker multiplier rule.