Publicación: Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems
Fecha
2019-04-19
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info:eu-repo/semantics/openAccess
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Springer Nature
Resumen
In this paper, we provide variants of the Ekeland variational principle for a type of approximate proper solutions of a vector equilibrium problem, whose final space is finite dimensional and partially ordered by a polyhedral cone. Depending on the choice of an approximation set that defines these solutions, we prove that they approximate suitably exact weak efficient/proper efficient/efficient solutions of the problem. The variants of the Ekeland variational principle are obtained for an unconstrained and also for a cone-constrained vector equilibrium problem, through a nonlinear scalarization, and expressed by means of the matrix that defines the ordering cone, which makes them easier to handle. At the end, the results are applied to multiobjective optimization problems, for which a related vector variational inequality problem is defined.
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Categorías UNESCO
Palabras clave
Ekeland variational principle, Vector equilibrium problems, Approximate proper solutions, Multiobjective optimization, Variational inequalities
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Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I