Informática para la optimización

[ES]Este material constituye el material de la asignatura Informática para la Optimización del cuarto curso del Grado en Economía, Facultad de Economía y Empresa, Universidad de Salamanca. El material esta desarrollado en Latex/Beamer y presenta los contenidos de un modo dinámico y con abundantes aplicaciones. Los temas desarrollados son: Introducción a la programación, optimización convexa diferenciable, programación lineal, programación cuadrática y optimización dinámica

Introducción a wxMaxima

[ES]wxMaxima es un programa que realiza cálculos matemáticos de forma tanto simbólica como numérica. Se encuentra disponible bajo licencia GNU GPL, y puede descargarse desde http://maxima.sourceforge.net/es/.El objetivo de esta guía es iniciar al alumno en el manejo de Maxima orientado a las matématicas de un primer curso de grado en Economía o Administración de Empresas. El contenido de este documento debe servir como apoyo y complemento a la asignaturas de Álgebra y Análisis Matemático

Preferences stability: A measure of preferences changes over time

Producción CientíficaTraditionally, preferences have been considered stable although there are growing evidences that such stability is a mere theoretical assumption. Attending to this fact, it should be interesting to measure how much stability preferences provide in order to improve decision making processes. Surprisingly, no research has been found on measuring preferences stability. To overcome this drawback, this paper proposes a novel approach for measuring the stability of preferences and also for improving understanding of current and future decisions. In order to be faithful to reality, this research considers decisions like complete pre-orders on a set of alternatives. Following this reasoning, this paper provides the general concept of decision stability measure as well as two specific measures: the local and the global decision stability measure. Moreover, the main features of the novel approach are examined, including several mathematical results on the behaviour of the proposed measure. And eventually, this contribution develops two real cases of study, with in-depth analysis of preferences behaviour and their stability over time. Specifically, the first one explores into the characteristics of Spanish citizens' voting behaviour and the second one attempts to analyse European citizens' preferences about passenger car market.Este trabajo forma parte del proyecto de investigación con financiación nacional: MEC-FEDER Grant ECO2016-77900-

Reaching social consensus family budgets: The Spanish case

The study of family budgets has been traditionally used to analyse consumers’ behaviour and estimate cost-of-living since the end of 19th century. Generally speaking, the computation of the budgets has been based on two different methodologies, the prescriptive and the descriptive method. Both present several drawbacks like the comparison among different areas, family types and over time. This paper proposes a new methodology for reaching family budgets, namely social consensus family budgets, to overcome such problems and examine the main features of the novel approach. The suggested method uses the minimization of the differences with respect to the consumer’s preferences to obtain a solution that summarizes single behaviour into a social preference. This approach is especially conceived for preferences on possibly related-expenditure groups. In addition, several algorithms are introduced to compute the social family budgets. Finally, the contribution includes the Spanish case as an example of reaching some social consensus family budgets in order to show the operational character and intuitive interpretation of the proposal approach.Este trabajo forma parte del proyecto de investigación con financiación nacional: MEC-FEDER Grant ECO2016-77900-

A reduced basis for a local high definition wind model

In this paper we present an application of the reduced basis method to a local high definition adjusted wind model. The model provides a precise description of the wind in 3D and takes into account topography and thermal gradients on the surface by solving only 2D linear equations; the buoyancy forces, slope effects, and mass conservation are also considered. The wind field is adjusted to the point measurements through an optimal control problem in which the wind flux acts as a control on the boundary. In order to use a reduced basis method, we consider an affine decomposition in terms of the parameter related to the friction coefficient and the wind measures at some given observation points. We also design an a posteriori error estimator that is needed to conduct our reduced basis process. Finally, two numerical examples are presented: a test problem and a real-data scenario, we corroborate the correct behavior of the method in both cases.Ministerio de Economía y Competitividad del Gobierno de España; FONDECYT N1140392, CONICYT; Basal CMM U. de Chile

Augmented mixed finite element method for the Oseen problem: A priori and a posteriori error analyses

We propose a new augmented dual-mixed method for the Oseen problem based on the pseudostress–velocity formulation. The stabilized formulation is obtained by adding to the dual-mixed approach suitable least squares terms that arise from the constitutive and equilibrium equations. We prove that for appropriate values of the stabilization parameters, the new variational formulation and the corresponding Galerkin scheme are well-posed, and a Céa estimate holds for any finite element subspaces. We also provide the rate of convergence when each row of the pseudostress is approximated by Raviart–Thomas or Brezzi–Douglas–Marini elements and the velocity is approximated by continuous piecewise polynomials. Moreover, we derive a simple a posteriori error estimator of residual type that consists of two residual terms and prove that it is reliable and locally efficient. Finally, we include several numerical experiments that support the theoretical results.Dirección de Investigación of the Universidad Católica de la Santísima Concepción (Chile) y CONICYT-Chile FONDECYT; Ministerio de Ciencia e Innovación del Gobierno de España

Space-Time adaptive algorithm for the mixed parabolic problem

Se presenta una estimación a posteriori del error para el problema parabólico lineal, y se diseña el correspondiente algoritmo de adaptación de malla y paso de tiempo. Para la discretización espacial se utiliza el elemento de Raviart-Thomas de menor orden y para la integración temporal la aproximación de Galerkin discontinua con paso variable. Se aplican los métodos numéricos desarrollados a varios problemas significativos que muestran la eficiencia del algoritmo desarrollado.In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient and reliable

Space-Time adaptive algorithmfor the mixed parabolic problem

Se presenta una estimación a posteriori del error para el problema parabólico lineal, y se diseña el correspondiente algoritmo de adaptación de malla y paso de tiempo. Para la discretización espacial se utiliza el elemento de Raviart-Thomas de menor orden y para la integración temporal la aproximación de Galerkin discontinua con paso variable. Se aplican los métodos numéricos desarrollados a variosproblemas significativos que muestran la eficiencia del algoritmodesarrollado.In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient and reliable

A downscale wind forecasting method based on WRF-HDMW coupling

[EN]In this paper, we propose a wind prediction strategy based on a mesoscale-microscale coupling technique. We will use the Weather Research and Forecast (WRF) [3] prediction as input data for the High Wind Defintion Model (HWDM) [2] to yield the forecast on a wind farm.Junta de Castilla y león; Fondos FEDE

A GIS-based fire spread simulator integrating a simplified physical wildland fire model and a wind field model

[EN]This article discusses the integration of two models, namely, the Physical Forest Fire Spread (PhFFS) and the High Definition Wind Model (HDWM), into a Geographical Information System-based interface. The resulting tool automates data acquisition, preprocesses spatial data, launches the aforementioned models and displays the corresponding results in a unique environment. Our implementation uses the Python language and Esri’s ArcPy library to extend the functionality of ArcMap 10.4. The PhFFS is a simplified 2D physical wildland fire spread model based on conservation equations, with convection and radiation as heat transfer mechanisms. It also includes some 3D effects. The HDWM arises from an asymptotic approximation of the Navier–Stokes equations, and provides a 3D wind velocity field in an air layer above the terrain surface. Both models can be run in standalone or coupled mode. Finally, the simulation of a real fire in Galicia (Spain) confirms that the tool developed is efficient and fully operational.Junta de Castilla y León; Fundación General de la Universidad de Salamanc