Person:
Huerga Pastor, Lidia

Loading...
Profile Picture
Email Address
ORCID
0000-0002-6634-3482
Birth Date
Research Projects
Organizational Units
Job Title
Last Name
Huerga Pastor
First Name
Lidia
Name

Search Results

Now showing 1 - 5 of 5
  • Publication
    A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization
    (Springer Nature, 2020-11-18) Jiménez, B.; Luc, D. T.; Novo, V.; Huerga Pastor, Lidia
    In this paper, we introduce some new notions of quasi efficiency and quasi proper efficiency for multiobjective optimization problems that reduce to the most important concepts of approximate and quasi efficient solutions given up to now. We establish main properties and provide characterizations for these solutions by linear and nonlinear scalarizations. With the help of quasi efficient solutions, a generalized subdifferential of a vector mapping is introduced, which generates a number of approximate subdifferentials frequently used in optimization in a unifying way. The generalized subdifferential is related to the classical subdifferential of real functions by the method of scalarization. An application of generalized subdifferential to express optimality conditions for quasi efficient solutions is also given.
  • Publication
    Continuity of a scalarization in vector optimization with variable ordering structures and application to convergence of minimal solutions
    (Taylor & Francis, 2022-05-30) Jiménez, B.; Novo, V.; Vílchez, A.; Huerga Pastor, Lidia
    We consider a scalarization function, which was introduced by Eichfelder [Variable ordering structures in vector optimization. Berlin: Springer-Verlag; 2014 (Series in vector optimization)], based on the oriented distance of Hiriart–Urruty with respect to a general variable ordering structure (VOS). We first study the continuity of the composition of a set-valued map with the oriented distance. Then, using the obtained results, we study the continuity of the scalarization function by extending some concepts of continuity for cone-valued maps. As an application, convergence in the sense of Painlevé–Kuratowski of sets of weak minimal solutions is provided, with the vector criterion and a VOS. Illustrative examples are also given.
  • Publication
    Necessary Conditions for Nondominated Solutions in Vector Optimization
    (Springer Nature, 2020-08-07) Bao, Truong Q.; Jiménez, B.; Novo, V.; Huerga Pastor, Lidia
    In this paper, we study characterizations and necessary conditions for nondominated points of sets and nondominated solutions of vector-valued functions in vector optimization with variable domination structure. We study not only the case, where the intersection of all the involved domination sets has a nonzero element, but also the case, where it might be the singleton. While the first case has been studied earlier, the second case has not, to the best of our knowledge, done yet. Our results extend and improve the existing results in vector optimization with a fixed ordering cone and with a variable ordering structure.
  • Publication
    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::virtual::4610::600; Huerga Pastor, Lidia; Huerga Pastor, Lidia; 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.
  • Publication
    New Notions of Proper Efficiency in Set Optimization with the Set Criterion
    (Springer Nature, 2022-09-17) Jiménez, B.; Novo, V.; Huerga Pastor, Lidia
    In this paper, we introduce new notions of proper efficiency in the sense of Henig for a set optimization problem by using the set criterion of solution. The relationships between them are studied. Also, we compare these concepts with the homologous ones given by considering the vector criterion. Finally, a Lagrange multiplier rule for Henig proper solutions of a set optimization problem with a cone constraint is obtained under convexity hypotheses. Illustrative examples are also given.