Limit Behavior of Approximate Proper Solutions in Vector Optimization
In the framework of a vector optimization problem, we provide conditions for approximate proper solutions to tend to exact weak/efficient/proper solutions when the error tends to zero. This limit behavior depends on an approximation set that is used to define the approximate proper efficient solutio...
| Autores: | , , , |
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| 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:20.500.14468/12546 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/12546 |
| Access Level: | acceso abierto |
| Palabra clave: | vector optimization approximate efficiency approximate proper efficiency dilating cone approximating family of cones |
| Sumario: | In the framework of a vector optimization problem, we provide conditions for approximate proper solutions to tend to exact weak/efficient/proper solutions when the error tends to zero. This limit behavior depends on an approximation set that is used to define the approximate proper efficient solutions. We also study the special case when the final space of the vector optimization problem is normed, and more particularly, when it is finite dimensional. In these specific frameworks, we provide several explicit constructions of dilating ordering cones and approximation sets that lead to the desired limit behavior. In proving our results, new relationships between different concepts of approximate proper efficiency are stated. |
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