Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.

The autobiography of John Fritz.

Mode of access: Internet.

Nonsmooth continuous-time optimization problems: Necessary conditions

We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Estratégias para resolução do problema MPEC

Pós-graduação em Matemática - IBILCE

The art to keep in touch: The ''good use'' of Lagrange multipliers

Physically-based modeling for computer animation allows to produce more realistic motions in less time without requiring the expertise of skilled animators. But, a computer animation is not only a numerical simulation based on classical mechanics since it follows a precise story-line. One common way to define aims in an animation is to add geometric constraints. There are several methods to manage these constraints within a physically-based framework. In this paper, we present an algorithm for constraints handling based on Lagrange multipliers. After few remarks on the equations of motion that we use, we present a first algorithm proposed by Platt. We show with a simple example that this method is not reliable. Our contribution consists in improving this algorithm to provide an efficient and robust method to handle simultaneous active constraints.

New variational principles for systems of partial differential equations

The question of finding variational principles for coupled systems of first order partial differential equations is considered. Using a potential representation for solutions of the first order system a higher order system is obtained. Existence of a variational principle follows if the original system can be transformed to a self-adjoint higher order system. Existence of variational principles for all linear wave equations with constant coefficients having real dispersion relations is established. The method of adjoining some of the equations of the original system to a suitable Lagrangian function by the method of Lagrange multipliers is used to construct new variational principles for a class of linear systems. The equations used as side conditions must satisfy highly-restrictive integrability conditions. In the more difficult nonlinear case the system of two equations in two independent variables can be analyzed completely. For systems determined by two conservation laws the side condition must be a conservation law in addition to satisfying the integrability conditions.

Um estudo da atenção primária à saúde mediante o indicador: Internações por condições sensíveis à atenção ambulatorial (CSAA)

A Atenção Primária à Saúde - APS é reconhecida como o nível fundamental e porta de entrada do sistema de atenção à saúde, sendo o lugar adequado onde pode ser atendida e resolvida a maior parte dos problemas de saúde. É considerada pela OMS como a principal proposta de modelo assistencial. Essa importância da APS leva a necessidade de pesquisas avaliativas dos seus resultados para adequação e melhoria de políticas e planos de ação delineados em relação à mesma. Pesquisas internacionais e nacionais são realizadas, nas quais indicadores relativos às atividades hospitalares estão sendo empregados com o objetivo de medir resultados como efetividade e acesso da APS. Um desses indicadores, desenvolvido por John Billings da Universidade de Nova York, na década de 90, consiste nas condições pelas quais as internações hospitalares por Condições Sensíveis à Atenção Ambulatorial (CSAA) deveriam ser evitadas caso os serviços da APS fossem efetivos e acessíveis. Utilizando-se o SIH-AIH/2008 e a lista brasileira de Internações por Condições Sensíveis a Atenção Primária, publicada em 2008, a proposta do presente trabalho é a de estudar os cuidados primários à saúde baseando-se nas ICSAA, na área urbana da cidade de Juiz de Fora-MG. Buscou-se responder sobre os efeitos que ocorrem nessas internações a partir das características individuais dos pacientes, das características das Unidades Básicas de Saúde-UBS (infraestrutura, produção e modelos assistenciais) e das condições sócio-econômicas/ambientais das áreas cobertas por UAPS e descobertas (sem UAPS), com a utilização de modelos multiníveis logísticos com intercepto aleatório. Buscou-se conhecer, também, a distribuição espacial das taxas padronizadas por idade das ICSAA nessas áreas e suas associações com as variáveis contextuais, utilizando-se ferramentas da análise espacial. Os resultados do presente trabalho mostraram que a porcentagem de internações por CSAA, foi de 4,1%. Os modelos assistenciais ESF e o Modelo Tradicional, base da organização da atenção primária no Brasil, não apresentaram no município, impacto significativo nas ICSAA, somente na forma de áreas descobertas tendo como referência as áreas cobertas. Também não foram significativas as variáveis de infraestrutura e produção das UAPS. Os efeitos individuais (idade e sexo) nas ICSAA foram significativos, apresentando probabilidades de significância menores que 1%, o mesmo acontecendo com o Índice de Desenvolvimento Social-IDS, que contempla as condições sociais, econômicas e ambientais das áreas analisadas. A distribuição espacial das taxas padronizadas por idade apresentou padrão aleatório e os testes dos Multiplicadores de Lagrange não foram significativos indicando o modelo de regressão clássico (MQO) como adequado para explicar as taxas em função das variáveis contextuais. Para a análise conjunta das áreas cobertas e descobertas foram fatores de risco: a variável econômica (% dos domicílios com renda até 2 SM), áreas descobertas tendo como referência as áreas cobertas e a região nordeste do município. Para as áreas cobertas as variáveis de produção das UAPS, econômica e a região nordeste apresentaram como fator de risco para as taxas de internação por CSAA.

Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms

We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

A “REVOLTA” DE JEÚ E A ESTELA DE DÃ: Um Estudo Em 2 Reis 10,28-36

A pesquisa tem por objetivo trabalhar o evento da Revolta de Jeú, em conjunto com a Estela de Dã, tendo como ponto de partida para tal, a exegese da perícope de 2 Reis 10-28,36. A história Deuteronomista apresenta o ato da Revolta de Jeú como sendo um feito demasiadamente importante, na restauração do culto a Javé em Israel, a partir de um contexto onde o culto a outras divindades, em Israel Norte, estava em pleno curso. No entanto, a partir da análise conjunta da Estela de Dã, que tem como provável autor o rei Hazael de Damasco, somos desafiados a ler esta história pelas entrelinhas não contempladas pelo texto, que apontam para uma participação ativa de Hazael, nos desfechos referentes a Revolta de Jeú, como sendo o responsável direto que proporcionou a subida de Jeú ao trono em Israel, clarificando desta forma este importante período na história Bíblica. Para tal análise, observar-se-á três distintos tópicos, ligados diretamente ao tema proposto: (1) A Revolta de Jeú e a Redação Deuteronomista, a partir do estudo exegético da perícope de 2 Reis 10,28-36, onde estão descritas informações pontuais sobre período em que Jeú reinou em Israel; (2) Jeú e a Estela de Dã, a partir da apresentação e análise do conteúdo da Estela de Dã, tratando diretamente dos desdobramentos da guerra em Ramote de Gileade, de onde se dá o ponto de partida à Revolta de Jeú; e por fim (3) O Império da Síria, onde a partir da continuidade da análise do conteúdo da Estela de Dã, demonstraremos a significância deste reino, além de apontamentos diretamente ligados ao reinado de Hazael, personagem mui relevante no evento da Revolta de Jeú.

John Frazer

John Frazer, Professor, trained at the Architectural Association, taught first at Cambridge University and then the AA in the 1970s and again in the '90s. He was Head of School of Design Research History and Criticism at the University of Ulster in the 1980s, he also ran a systems and design consultancy with his wife Julia (including projects for Cedric Price and Walter Segal) and was founder and chairman of Autographics software. He is currently Swire Chair Professor and Head of School of Design in Hong Kong.----- This is a very personal perspective on a concept of universal and future significance. It is personal, both is the sense that it is an unashamedly biased view of both the significance of the project, and the nature of that significance and because the author was personally involved as one of the consultants on GENERATOR and subsequently involved Cedric Price in its educational application at the Architectural Association. GENERATOR is still very much alive and was still developing whilst this chapter was being written.

Concerning the house museum and the picturesque landscape in the work of Sir John Soane : with raw hints for post-heritage museum space

The picturesque aesthetic in the work of Sir John Soane, architect and collector, resonates in the major work of his very personal practice – the development of his house museum, now the Soane Museum in Lincoln’s Inn Fields in London. Soane was actively involved with the debates, practices and proponents of picturesque and classical practices in architecture and landscape and his lectures reveal these influences in the making of The Soane, which was built to contain and present diverse collections of classical and contemporary art and architecture alongside scavenged curiosities. The Soane Museum has been described as a picturesque landscape, where a pictorial style, together with a carefully defined itinerary, has resulted in the ‘apotheosis of the Picturesque interior’. Soane also experimented with making mock ruinscapes within gardens, which led him to construct faux architectures alluding to archaeological practices based upon the ruin and the fragment. These ideas framed the making of interior landscapes expressed through spatial juxtapositions of room and corridor furnished with the collected object that characterise The Soane Museum. This paper is a personal journey through the Museum which describes and then reviews aspects of Soane’s work in the context of contemporary theories on ‘new’ museology. It describes the underpinning picturesque practices that Soane employed to exceed the boundaries between interior and exterior landscapes and the collection. It then applies particular picturesque principles drawn from visiting The Soane to a speculative project for a house/landscape museum for the Oratunga historic property in outback South Australia, where the often, normalising effects of conservation practices are reviewed using minimal architectural intervention through a celebration of ruinous states.