Persona:
Huerga Pastor, Lidia

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0000-0002-6634-3482
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Huerga Pastor
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Lidia
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2018 - 20193
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Fecha de finalización: 2019 × search.filters.applied.f.itemDepartamento: Matemática Aplicada I ×

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Mostrando 1 - 3 de 3
  • Miniatura
    Publicación
    Limit Behavior of Approximate Proper Solutions in Vector Optimization
    (Society for Industrial and Applied Mathematics, 2019) Gutiérrez, C.; Novo, V.; Huerga Pastor, Lidia; Sama Meige, Miguel Ángel
    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.
  • Miniatura
    Publicación
    Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems
    (Springer Nature, 2019-04-19) Hai, L. P.; Khanh, P. Q.; Novo, V.; Huerga Pastor, Lidia
    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.
  • Miniatura
    Publicación
    Approximate solutions of vector optimization problems via improvement sets in real linear spaces
    (Springer Nature, 2018-04) Gutiérrez, C.; Jiménez, B.; Novo, V.; Huerga Pastor, Lidia
    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.