An interior point technique for nonlinear optimization

Projet MODULEFWe propose an approach for the minimization of a smooth function under smooth equality and inequality constraints by interior points algorithms. It consists on the iterative solution, in the primal and dual variables, of Karush-Kuhn-Tucker first order optimality conditions. Based on this approach, different order algorithms can be obtained. To introduce the method, in a first stage we consider the inequality constrained problem and present a globally convergent basic algorithm. Particular first order and quasi-Newton versions of the algorithm are also stated. In a second stage, the general problem is consider and a basic algorithm obtained. This method is simple to code, since it does not involve the solution of quadratic programs but merely that of linear systems of equations. Several applications show that it is also strong and efficient

Um sistema automático de projeto de estruturas ótimas

A computer system for the automatic sizing of large-scale structures is developed, making use of an "optimali ty cri terion" algori thm, where inequali ty constraints are treated with the aid of slack-variables. Attention is focused on fixed geometry structures which can be idealized using finite elements. Multiple loading conditions are also considered. Element stresses, nodal displacements, and buckling of axialy compressed elements are considered as constraints. Methods of structural analysis, calculation of gradients of response functions and the general organization of the system are ihoroughly described. The mathematical foundations of the optimization algorithm,are also showed in condensed form. The automatic design of a variety of structural systems, allows to conclude that the system performance is efficient and competitive.Se desarrolla un sistema computacional, que dimensiona enforma automática, estructuras óptimas de gran porte. El mismo utiliza un algoritmo de optimización de tipo "Criterio de Optimalidad", en el que se tratan las restricciones de desigualdad, mediante la definición de variables de desvío. El sistema considera estructuras discretizables me diante la utilización de elementos finitos, sometidas a varias estados de carga y de geometría prefijada por el proyectista. Las restricciones incluídas son aquellas que limitan desplazamientos nodales y tensiones en los elementos, adicionando la consideración de pandeo, en los elementos axiales sometidos a compresión. Se describen los métodos de análisis estructural utilizados y el cálculo de los gradientes de las funciones de respuesta, al igual que la organización general del sistema. También se presentan, enforma condensada, los fundamentos matemáticos del algoritmo de optimización. La resolución de diversos ejemplos estructurales, permite observar que el sistema actúa enforma eficiente y competitiva.É desenvolvido um sistema computacional, que dimensiona automáticamente estruturas Ótimas de grande porte. Este utiliza um algoritmo de otimização do tipo "Critério de Otimalidade", no qual se tratam as restrições de desigualdade, mediante a definição de variáveis de desvio. O sistema considera estruturas discretizáveis mediante a utilização de elementos finitos, submetidas a vários estados de carga e de geometria prefixada pelo projetista. As restrições incluídas são aquelas que limitam deslocamentos nodais e tensões nos elementos, adicionando a consideração da flambagem nos elementos axiais submetidos a compressão. São descritos os métodos de análise estrutural utilizados, o cálculo dos gradientes das funções de resposta e também a organização geral do sistema. Também se apresentam com forma condensada, os fundamentos matemáticos do algoritmo de otimização. A resolução de diversos exemplos estruturais, permite observar que o sistema atua de forma eficiente e competitiva

Design of laminated structures using piezoelectric materials

Composite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the offer of potential benefits in a wide range of engineering applications such as vibration and noise supression, shape control and precisition positioning. This paper presents a finit element formulation based on classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezsoelectric elementlayer or patch, witch are surface bonded on the laminate. An optimization of the patches position is performed to maximize the piezoelectric actuators efficiency as well as, the electric potential distribuition is search to reach the specified structure transverse displacement distribuition (shape control). A gradient based algorithm is used for this purpose. The model is applied in the optimization of illustrative laminated plate cases, and the results are presented and discussed

Shape control of laminated panels using piezoelectric actuators

This paper presents a finite element formulation based on the classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as actuators.The finite element model is a single layer trinaguular nonconforming plate/shell element with 18 degrees of fredom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element elemenet layer or patch. An optimization of the patches position is perfomed to maximize the piezoelectric actuators efficiency as well as,the electric potential distribution is serach to reach the specified strusctura transverse displacement distribution is search to reach the specified structures trsnsverse displacement distribution (shape control). A gradient based algorithm is used for this purpose.Results are presented and discussed

Impacto de los cambios tecnológicos en los modelos de negocios de las industrias de cultura y ocio en España - El caso de los museos y clubes de fútbol

En una primera instancia puede resultar sorprendente tratar en el mismo artículo organizaciones tan diferentes como los museos y los clubes de futbol. Sin embargo, en una mirada de más detalle se puede ver que ambas organizaciones cuentan con una relación muy estrecha en el plano emocional con sus seguidores. A partir de esta relación se analizan los múltiples cambios tecnológicos que pueden afectar a este sector, considerando los posibles efectos en modelos de negocio de éxito que se puedan adoptar en el futuro. El articulo culmina con una reflexión sobre las alternativas que el sector puede adoptar para continuar evolucionando sus modelos de negocio aprovechando los cambios tecnológicos identificados

Inductor shape optimization for electromagnetic casting

The design of inductors in electromagnetic shaping of molten metals consists of looking for the position and the shape of a set of electric wires such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. In this paper we formulate an inverse optimization problem where the position and shape of the inductors are defined by a set of design variables. The solution of this problem correspond to the optimal design, i.e., the shape of the liquid metal is as close as possible to the target shape. In a first formulation of the inverse optimization problem we minimize the difference between the target and the equilibrium shapes while in a second approach we minimizes the $L^2$ norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. Geometric constraints that prevent the inductors to penetrate into the liquid metal are considered in both formulations. The optimization problems are solved using FAIPA, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches

Determinación de los parámetros de campo para la adquisición 3D de datos sísmicos

Las etapas de adquisición, procesamiento e interpretación de los datos sísmicos en la exploración de hidrocarburos están estrechamente relacionadas. Los errores cometidos en la determinación de los parámetros de campo para la registración de los datos, difícilmente puedan ser subsanados por el procesamiento y por lo tanto, terminan condicionando a la interpretación. Dado que la mejor elección de los parámetros del tendido sísmico es la que logra el propósito de la exploración geofísica minimizando costos y tiempo en la captura y procesamiento de los datos, el presente trabajo aborda esta problemática como un proceso de optimización. La idea es hallar el mínimo de una función objetivo que representa los costos de un relevamiento terrestre 3D para un tendido ortogonal, sujeta a restricciones operacionales (movimientos de fuentes y receptores) y requerimientos geofísicos (suma o fold, offset y azimutes). Los resultados se obtienen mediante la aplicación del algoritmo: FAIPA (Feasible Arc Interior Point Algorithm), pudiendo comparar esta técnica con otros procedimientos similares ya publicados.3D seismic survey design in hydrocarbon exploration is related to processing and interpretation. In this paper, we invite to recommend survey design parameters, based on an optimization method such as the FAIPA (Feasible Arc Interior PointAlgorithm). The seismic data has to achieve the geophysical objetive and satisfy geophysical and operational constraints (fold, offset, azimuths, shots and receivers moved/day, etc.) while minimizing the cost and time of adquisition and processing. 3D design examples illustrate the implementation of iterative algorithm and allows compare with another published optimization methods.Material digitalizado en SEDICI gracias a la colaboración de la Facultad de Ciencias Astronómicas y Geofísicas (UNLP).Asociación Argentina de Geofísicos y Geodesta

A New Interior Point Algorithm for Nonlinear Complementarity Problems

The complementarity problem consists in finding x F (x)=0, . Complementarity problems are involved in several applications in engineering, economy and di#erent branches of physics . We mention contact problems and dynamics of multiple bodies systems in solid mechanics. In this paper we present a new feasible interior point algorithm for nonlinear complementarity problems. This algorithm begins at a point that verifies the inequality conditions of the problem and generates a sequence of points that also verify them. The numerical results obtained with several numerical test problems, and also with contact problems, are presented. Here the problems were solved very efficiently when compared with other methods. The present approach is also very strong; all the results were obtained with the same set of parameters