Approximate solutions of vector optimization problems via improvement sets in real linear spaces

We deal with a constrained vector optimization problem between real linear spaces without assuming any topology and by considering an ordering defined through an improvement set E. We study E-optimal and weak E-optimal solutions and also proper E-optimal solutions in the senses of Benson and Henig....

Descripción completa

Detalles Bibliográficos
Autores: Gutiérrez, C., Jiménez, B., Novo, V., Huerga Pastor, Lidia
Tipo de recurso: artículo
Fecha de publicación:2018
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:20.500.14468/12543
Acceso en línea:https://hdl.handle.net/20.500.14468/12543
Access Level:acceso abierto
Palabra clave:Vector optimization
Improvement set
Approximate weak efficiency
Approximate proper efficiency
Nearly E-subconvexlikeness
Linear scalarization
Lagrange multipliers
algebraic interior
Vector closure
Descripción
Sumario:We deal with a constrained vector optimization problem between real linear spaces without assuming any topology and by considering an ordering defined through an improvement set E. We study E-optimal and weak E-optimal solutions and also proper E-optimal solutions in the senses of Benson and Henig. We relate these types of solutions and we characterize them through approximate solutions of scalar optimization problems via linear scalarizations and nearly E-subconvexlikeness assumptions. Moreover, in the particular case when the feasible set is defined by a cone-constraint, we obtain characterizations by means of Lagrange multiplier rules. The use of improvement sets allows us to unify and to extend several notions and results of the literature. Illustrative examples are also given.