Papers by Gabriel Ruiz-Garzón
Journal of Inequalities and Applications
This work is included in the search of optimality conditions for solutions to the scalar interval... more This work is included in the search of optimality conditions for solutions to the scalar interval optimization problem, both constrained and unconstrained, by means of second-order optimality conditions. As it is known, these conditions allow us to reject some candidates to minima that arise from the first-order conditions. We will define new concepts such as second-order gH-derivative for interval-valued functions, 2-critical points, and 2-KKT-critical points. We obtain and present new types of interval-valued functions, such as 2-pseudoinvex, characterized by the property that all their second-order stationary points are global minima. We extend the optimality criteria to the semi-infinite programming problem and obtain duality theorems. These results represent an improvement in the treatment of optimization problems with interval-valued functions.
Computational and Applied Mathematics
This paper aims to obtain new Karush–Kuhn–Tucker optimality conditions for solutions to semi-infi... more This paper aims to obtain new Karush–Kuhn–Tucker optimality conditions for solutions to semi-infinite interval equilibrium problems with interval-valued objective functions. The Karush–Kuhn–Tucker conditions for the semi-infinite interval programming problem are particular cases of those found in this paper for constrained equilibrium problem. We illustrate this with some examples. In addition, we obtain solutions to the interval equilibrium problem in the unconstrained case. The results presented in this paper extend the corresponding results in the literature.
The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmo... more The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush--Kuhn--Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash's critical and equilibrium points coincide in the case of invex payoff functions.
This work is intended to lead a study of necessary and sufficient optimality conditions for scala... more This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new charac...
Suma Revista Sobre Ensenanza Y Aprendizaje De Las Matematicas, 2001
Durante la noche del dia 23 de noviembre de 1654, aproximadamente entre las diez y media y las do... more Durante la noche del dia 23 de noviembre de 1654, aproximadamente entre las diez y media y las doce y media de la noche, experimento Pascal una especie de extasis religioso que lo impulso a abandonar la matematica para dedicarse a la teologia. Afortunadamente, una noche de 1658 en que un dolor de muelas u otra dolencia le impedia dormir, decidio dedicarse al estudio de la cicloide. Milagrosamente el dolor ceso, lo que interpreto Pascal como un signo de que el estudio de la matematica agradaba a Dios.
Epsilon Revista De La Sociedad Andaluza De Educacion Matematica Thales, 1990
Xxv Congreso Nacional De Estadistica E Investigacion Operativa Vigo 4 7 De Abril De 2000 2000 Isbn 84 8158 152 6 Pags 519 520, 2000
Xxxi Congreso Nacional De Estadistica E Investigacion Operativa V Jornadas De Estadistica Publica Murcia 10 13 De Febrero De 2009 Libro De Actas 2009 Isbn 978 84 691 8159 1, 2009
Es conocido que la condicion de KT-invexidad para funciones de nidas en un Problema de Control e... more Es conocido que la condicion de KT-invexidad para funciones de nidas en un Problema de Control es una condicion necesaria y su ciente para que todos los puntos de Kuhn- Tucker sean soluciones optimales. El objetivo de esta comunicacion es doble. Por una parte establecer condiciones de dualidad debil, fuerte e inversa entre la formulacion de un Problema de Control y un problema dual del mismo del tipo Mond-Weir. Por otra parte mostraremos alguna de las aplicaciones industriales de los problemas de control, como es el dise~no de vehculos autonomos.
Xxvi Congreso Nacional De Estadistica E Investigacion Operativa Ubeda 6 9 De Noviembre De 2001 2001 Isbn 84 8439 080 2, 2001
En este trabajo veremos las relaciones existentes entre los problemas cuasi variacionales vectori... more En este trabajo veremos las relaciones existentes entre los problemas cuasi variacionales vectoriales y los problemas de optimizacion vectoriales, llegando a identificar los puntos criticos vectoriales, los puntos debilmente eficientes y las soluciones del Problema de Desigualdad Cuasi Variacional Vectorial Debil, bajo condiciones de pseudo invexidad.
Taiwanese Journal of Mathematics
In this article, our efforts focus on finding the conditions for the existence of solutions of Mi... more In this article, our efforts focus on finding the conditions for the existence of solutions of Mixed Stampacchia Variational Inequality Interval-valued Problem on Hadamard manifolds with monotonicity assumption by using KKM mappings. Conditions that allow us to prove the existence of equilibrium points in a market of perfect competition. We will identify solutions of Stampacchia variational problem and optimization problem with the interval-valued convex objective function, improving on previous results in the literature. We will illustrate the main results obtained with some examples and numerical results.
The aim of this paper is to show some applicable results to multiobjective optimization problems ... more The aim of this paper is to show some applicable results to multiobjective optimization problems and the role that the Generalized Convexity plays in them. The study of convexity for sets and functions has special relevance in the search of optimal functions, and in the development of algorithms for solving optimization problems. However, the absence of convexity implies a total loss of effectiveness of the Optimization Theory methods, ie, the results are being verified under less stringent conditions, it was what became known as Generalized convexity. The literature generated around this topic has demonstrated its importance both from a theoretical point of view as practical, but it has also generated an enormous amount of papers with little scientific input.
Fuzzy Optimization and Decision Making, 2017
Fuzzy numbers have been applied on decision and optimization problems in uncertain or imprecise e... more Fuzzy 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.
Historia De La Probabilidad Y De La Estadistica Vi 2012 Isbn 9788436264074 Pags 331 344, 2012
Epsilon Revista De La Sociedad Andaluza De Educacion Matematica Thales, 1999
Epsilon Revista De La Sociedad Andaluza De Educacion Matematica Thales, 1989
Beio Boletin De Estadistica E Investigacion Operativa, 2013
The aim of this paper is to make a historical review on probabilistic arguments, principally prov... more The aim of this paper is to make a historical review on probabilistic arguments, principally provided by Alphonse Bertillon, with the aim of sentencing the Jewish captain Alfred Dreyfus for espionage, as well as the arguments against the sentence given to Henri Poincaré. Bertillon was the creator of anthropometry as a method of identifying criminals. In contrast to the method developed by Bertillon, Francis Galton was a strong advocate of the method of fingerprint with probabilistic arguments to carry out identifications.
Applied Mathematics and Computation, 2015
In this work, first we introduce several notions of invexity and pseudoinvexity for a locally Lip... more In this work, first we introduce several notions of invexity and pseudoinvexity for a locally Lipschitz function by means of the generalized Jacobian. We study relationships between these concepts, in particular the implications between preinvexity and invexity. Next, we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite-dimensional (non necessarily Pareto) vector optimization problems with locally Lipschitz objective functions through solutions of vector variational-like inequality problems. These conditions are stated via the generalized Jacobian and under pseudoinvexity hypotheses, and they show that a vector optimization problem can be reformulated as a vector variational-like inequality problem. This work extends and improves several previous papers, where the objective function of the vector optimization problem is assumed to be differentiable, or being locally Lipschitz, the authors consider the componentwise subdifferential based on the Clarke's generalized gradients of the components of the objective function. Throughout the paper some simple examples are given in order to illustrate the main concepts and results.
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Papers by Gabriel Ruiz-Garzón