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Approximate solutions of multiobjective optimization problems

César Gutiérrez Vaquero
Departamento de Matemática Aplicada
Universidad da Valladolid
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Lidia Huerga Pastor
Departamento de Matemática Aplicada I
Universidad Nacional de Educación a Distancia
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  • Abstract
    This paper collects some recently published results on approximate solutions of infinite dimensional vector optimization problems. Here, they are obtained in a finite dimensional framework with simple formulations and proofs, in order to get a self-contained and illustrative work. To be exact, a concept of approximate nondominated solution is presented, and its main properties are studied. After that, a general scalarization scheme is introduced to characterize this kind of solutions via suboptimal solutions of associated scalar optimization problems. Finally, a Kuhn-Tucker multiplier rule is stated in convex problems ordered by components, that characterizes the more popular type of ε-efficient solution of the literature.
  • Keywords: ε-efficiency, Scalarization, Order preserving property, Order representing property, ε-subgradient, Kuhn-Tucker condition.
  • AMS Subject classifications: 90C29, 90C46, 49J52.