Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems

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 s...

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Detalles Bibliográficos
Autores: Hai, L. P., Khanh, P. Q., Novo, V., Huerga Pastor, Lidia
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/12541
Acceso en línea:https://hdl.handle.net/20.500.14468/12541
Access Level:acceso abierto
Palabra clave:Ekeland variational principle
Vector equilibrium problems
Approximate proper solutions
Multiobjective optimization
Variational inequalities
Descripción
Sumario: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.