Persona: Huerga Pastor, Lidia
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Huerga Pastor
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Lidia
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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, LidiaWe 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.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, LidiaIn 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.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 ÁngelIn 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.Publicación New Notions of Proper Efficiency in Set Optimization with the Set Criterion(Springer Nature, 2022-09-17) Jiménez, B.; Novo, V.; Huerga Pastor, LidiaIn 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.Publicación 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, LidiaWe 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.Publicación Necessary Conditions for Nondominated Solutions in Vector Optimization(Springer Nature, 2020-08-07) Bao, Truong Q.; Jiménez, B.; Novo, V.; Huerga Pastor, LidiaIn 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.Publicación 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, LidiaIn 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.Publicación Soluciones propias aproximadas de problemas de optimización vectorial(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias. Departamento de Matemática Aplicada, 2014-10-23) Huerga Pastor, Lidia; Novo Sanjurjo, Vicente; Gutiérrez Vaquero, CésarSe introduce un concepto de solución propia aproximada de problemas de optimización vectorial. Esta noción se define con la finalidad de obtener un conjunto de soluciones aproximadas que represente bien al conjunto eficiente salvo un pequeño error, lo que se traduce en que el límite superior de Painlevé-Kuratowski del conjunto formado por estas soluciones, .cuando el error de precisión tiende a cero, está incluido en el conjunto de soluciones eficientes exacta.s. Esta propiedad esencial no es común en las nociones de eficiencia propia aproximada, de forma que, con frecuencia, estos conceptos pueden generar sucesiones de soluciones aproximadas que se alejan del conjunto eficiente tanto como se quiera, La memoria se vertebra. en tomo al estudio de estas soluciones. Concretamente, se .analizan sus propiedades y se caracterizan mediante esca]arización lineal bajo condiciones de convexidad generalizada. Además, se utilizan para definir un concepto de punto de silla. propio aproximado e introducir. y estudiar problemas duales aproximados y una e-subdiferencial propia de funciones vectoriales. Los problemas duales introducidos son ambos de tipo Lagrangiano. El primero se define mediante una Lagrangiana escalar y el segundo mediante una multifunción Lagrangiana, que generaliza las Lagrangianas vectoriales más importantes de la literatura. Se obtienen teoremas de dualidad débil y fuerte bajo condiciones de estabilidad y convexidad generalizada, que relacionan los maximales aproximados de cada problema dual con estas nuevas soluciones propias aproximadas del primal. La E-subdiferencial propia definida se caracteriza a través de E-subgradientes de funciones escalares, asumiendo condiciones de convexidad generalizada y es apropiada para tratar con sucesiones minimizantes. Finalmente, se prueban para estasubdiferencial propia aproximada reglas de cálculo de tipo Moreau-Rockafellar y reglas de la cadena.