Person: Hernández-Jiménez, Beatriz
Profesor/a Titular de Universidad
Universidad Pablo de Olavide
Economía, Métodos Cuantitativos e Historia Económica
Estadística e Investigación Operativa
Now showing 1 - 10 of 11
PublicationDifferent optimum notions for fuzzy functions and optimality conditions associated(Springer, 2017-03-15) Osuna-Gómez, Rafaela; Chalco-Cano, Yurilev; Ruíz-Garzón, Gabriel; Hernández-Jiménez, BeatrizFuzzy numbers have been applied on decision and optimization problems in uncertain or imprecise environments. In these problems, the necessity to define optimal notions for decision-maker’s preferences as well as to prove necessary and sufficient optimality conditions for these optima are essential steps in the resolution process of the problem. The theoretical developments are illustrated and motivated with several numerical examples. PublicationOptimality and duality on Riemannian manifolds(Mathematical Society of the Rep. of China, 2018-10) Ruíz-Garzón, Gabriel; Osuna-Gómez, Rafaela; Rufián-Lizana, Antonio; Hernández-Jiménez, BeatrizOur goal in this paper is to translate results on function classes that are characterized by the property that all the Karush-Kuhn-Tucker points are efficient solutions, obtained in Euclidean spaces to Riemannian manifolds. We give two new characterizations, one for the scalar case and another for the vectorial case, unknown in this subject literature. We also obtain duality results and give examples to illustrate it. PublicationOptimality Conditions for Nonregular Optimal Control Problems and Duality(Taylor & Francis, 2017-09-22) Osuna-Gómez, Rafaela; Vivanco-Orellana, Violeta; Rojas-Medar, Marko Antonio; Hernández-Jiménez, BeatrizWe define a new class of optimal control problems and show that this class is the largest one of control problems where every admissible process that satisfies the Extended Pontryaguin Maximum Principle is an optimal solution of nonregular optimal control problems. In this class of problems the local and global minimum coincide. A dual problem is also proposed, which may be seen as a generalization of the Mond–Weir-type dual problem, and it is shown that the 2-invexity notion is a necessary and suﬃcient condition to establish weak, strong, and converse duality results between a nonregular optimal control problem and its dual problem. We also present an example to illustrate our results. PublicationNecessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems(Springer, 2019-06-15) de Oliveira, Washington Alves; Rojas-Medar, Marko Antonio; Beato-Moreno, Antonio; Hernández-Jiménez, Beatriz PublicationA Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets(MPDI, 2021-04-28) Ruíz-Garzón, Gabriel; Beato-Moreno, Antonio; Osuna-Gómez, Rafaela; Hernández-Jiménez, BeatrizIn this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions. PublicationApproximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities(MPDI, 2020-12-10) Ruíz-Garzón, Gabriel; Osuna-Gómez, Rafaela; Rufián-Lizana, Antonio; Hernández-Jiménez, BeatrizThis article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated them with examples. We see the minimum requirements under which critical points, solutions of Stampacchia, and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we show an economical application, again using solutions of the variational problems to identify Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions. PublicationNecessary and sufficient conditions for interval-valued differentiability(Wiley, 2022-08-22) Osuna-Gómez, Rafaela; Mendonca da Costa, Tiago; Ruíz-Garzón, Gabriel; Hernández-Jiménez, BeatrizThis paper presents necessary and sufficient conditions for generalized Hukuhara differentiability of interval-valued functions and counterexamples of some equivalences previously presented in the literature, for which important results are based on. Moreover, applications of interval generalized Hukuhara differentiability are presented. PublicationQuasilinear approximation for interval-valued functions via generalized Hukuhara differentiability(Springer, 2022-04-20) Osuna-Gómez, Rafaela; Mendoça da Costa, Tiago; Chalco-Cano, Yurilev; Hernández-Jiménez, BeatrizIn this paper, a new generalized Hukuhara differentiability concept for interval-valued functions defined on Rn is proposed, which extends the classical Fréchet differentiability notion and provides an interval quasilinear approximation for an interval-valued function in a neighborhood of a point at which such function is gH-differentiable. Moreover, it overcomes the shortcomings generated by the use of the gH-differentiability concept previously presented in the literature, and this presents a good perspective on interval and fuzzy environments. Several properties of this new concept are investigated and compared with the previous concept properties. Furthermore, the gH-differentiability concept is extended for a fuzzy function, and its introduction is argued and illustrated with examples. PublicationAn approach based on the pseudospectral method for fractional telegraph equations(AIMS Press, 2023-10-26) Bin Jebreen, Haifa; Hernández-Jiménez, BeatrizWe aim to implement the pseudospectral method on fractional Telegraph equation. To implement this method, Chebyshev cardinal functions (CCFs) are considered bases. Introducing a matrix representation of the Caputo fractional derivative (CFD) via an indirect method and applying it via the pseudospectral method helps to reduce the desired problem to a system of algebraic equations. The proposed method is an effective and accurate numerical method such that its implementation is easy. Some examples are provided to confirm convergence analysis, effectiveness and accuracy. PublicationNew optimality conditions for multiobjective fuzzy programming problems(University of Sistan and Baluchestan, 2020-05-01) Osuna-Gómez, Rafaela; Chalco-Cano, Yurilev; Ruíz-Garzón, Gabriel; Hernández-Jiménez, BeatrizIn this paper we study fuzzy multiobjective optimization problems defined for $n$ variables. Based on a new $p$-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.