Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Improvement of a filters method in a derivative free optimization

Constraints nonlinear optimization problems can be solved using penalty or barrier functions. This strategy, based on solving the problems without constraints obtained from the original problem, have shown to be e ective, particularly when used with direct search methods. An alternative to solve the previous problems is the lters method. The lters method introduced by Fletcher and Ley er in 2002, , has been widely used to solve problems of the type mentioned above. These methods use a strategy di erent from the barrier or penalty functions. The previous functions de ne a new one that combine the objective function and the constraints, while the lters method treat optimization problems as a bi-objective problems that minimize the objective function and a function that aggregates the constraints. Motivated by the work of Audet and Dennis in 2004, using lters method with derivative-free algorithms, the authors developed works where other direct search meth- ods were used, combining their potential with the lters method. More recently. In a new variant of these methods was presented, where it some alternative aggregation restrictions for the construction of lters were proposed. This paper presents a variant of the lters method, more robust than the previous ones, that has been implemented with a safeguard procedure where values of the function and constraints are interlinked and not treated completely independently.

What is a fractional derivative?

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Os desafios da qualificação profissional pós-secundária não-superior (nível 4) para a inovação empresarial no contexto da União Europeia e dos países da OCDE

A maioria das nações mais desenvolvidas deve, em larga medida, a sua prosperidade à produtividade da sua força de trabalho. Esta produtividade relaciona-se, fundamentalmente, com dois aspectos essenciais. Por um lado, com o nível e adequação das qualificações e competências da população activa, as quais permitem desenvolver o empreendedorismo e criar riqueza e, por outro, com a qualidade e grau de sofisticação dos equipamentos, tecnologias, modelos de organização e sistemas de gestão de que as empresas dispõem. Nesta comunicação, elaborada por convite para apresentação na sessão comemorativa do 20º aniversário da AFTEM, no Porto, após a contextualização das exigências do mercado de trabalho em resultado da inovação empresarial e da emergência das economias baseadas no conhecimento, apresentam-se alguns estudos recentemente concluídos em diversos países e regiões da OCDE, nomeadamente, Austrália, Irlanda, Reino Unido e Escócia – nos quais se foca a necessidade de incrementar o nível de qualificações para responder às necessidades do tecido produtivo por forma a manter a competitividade da indústria e serviços desses países e regiões à escala global; em particular realça-se a importância de se aumentar a percentagem de população activa com nível 4 de qualificação profissional. Aborda-se, ainda, a situação da formação pós secundária não superior em Portugal (nível 4). Conclui-se, formulando algumas recomendações em termos de estratégias e de trabalho futuro com vista a dinamizar as oportunidades de qualificação de nível 4, em estreita articulação com as empresas, como forma de o tecido produtivo nacional dispor de níveis de qualificação de recursos humanos que permitam a mobilidade para novas actividades com maior valor acrescentado e, por esta via, atingir níveis de rentabilidade semelhante à dos restantes estados membros da UE e de outros países da OCDE.

Pronoun-dropping or zero anaphora in translation from german into portuguese

In this article I will analyse anaphoric references in German texts and their transaltion into Portuguese. I will take as main corpus Heinrich Böll's novel Haus ohne Hüter and its translation into Portuguese by Jorge Rosa with the title Casa Indefesa. I will concentrate on the use of personal pronouns and possessives in references to both people and objects in source text and target text and I will present patterns of symmetries and asymmetries. I will claim that asymmetries in the translation of such anaphoric references can be accounted for mainly by differences in the pronominal systems and verbal systems of both languages and by differences in the way each language marks theme/topic continuity/discontinuity in discourse. Issues related to style and the translation of anaphors will also be addressed. I will finally raise some questions related to ambiguous references which can not be solved within the scope of syntax or semantics, thus requiring pragmatic interpretation based on cultural knowledge/world knowledge.

The economics of language or how can language be an asset? General reflections on the European case and brief focus on the case of portuguese

In this paper, we will focus on the importance of languages as an asset to people and companies in knowledge-based society, giving special attention to the case of portuguese, not forgetting the role of Higher Education Institutions in preparing students to be part of the new creative multilingual and sucsessful class.

Sintonia de controladores baseada em Sistemas de Inferência Difusa

Este trabalho de pesquisa e desenvolvimento tem como fundamento principal o Conceito de Controlo por Lógica Difusa. Utilizando as ferramentas do software Matlab, foi possível desenvolver um controlador com base na inferência difusa que permitisse controlar qualquer tipo de sistema físico real, independentemente das suas características. O Controlo Lógico Difuso, do inglês “Fuzzy Control”, é um tipo de controlo muito particular, pois permite o uso simultâneo de dados numéricos com variáveis linguísticas que tem por base o conhecimento heurístico dos sistemas a controlar. Desta forma, consegue-se quantificar, por exemplo, se um copo está “meio cheio” ou “meio vazio”, se uma pessoa é “alta” ou “baixa”, se está “frio” ou “muito frio”. O controlo PID é, sem dúvida alguma, o controlador mais amplamente utilizado no controlo de sistemas. Devido à sua simplicidade de construção, aos reduzidos custos de aplicação e manutenção e aos resultados que se obtêm, este controlador torna-se a primeira opção quando se pretende implementar uma malha de controlo num determinado sistema. Caracterizado por três parâmetros de ajuste, a saber componente proporcional, integral e derivativa, as três em conjunto permitem uma sintonia eficaz de qualquer tipo de sistema. De forma a automatizar o processo de sintonia de controladores e, aproveitando o que melhor oferece o Controlo Difuso e o Controlo PID, agrupou-se os dois controladores, onde em conjunto, como poderemos constatar mais adiante, foram obtidos resultados que vão de encontro com os objectivos traçados. Com o auxílio do simulink do Matlab, foi desenvolvido o diagrama de blocos do sistema de controlo, onde o controlador difuso tem a tarefa de supervisionar a resposta do controlador PID, corrigindo-a ao longo do tempo de simulação. O controlador desenvolvido é denominado por Controlador FuzzyPID. Durante o desenvolvimento prático do trabalho, foi simulada a resposta de diversos sistemas à entrada em degrau unitário. Os sistemas estudados são na sua maioria sistemas físicos reais, que representam sistemas mecânicos, térmicos, pneumáticos, eléctricos, etc., e que podem ser facilmente descritos por funções de transferência de primeira, segunda e de ordem superior, com e sem atraso.

Determination of tartaric acid in wines by FIA with tubular tartrate-selective electrodes

A flow injection analysis (FIA) system comprising a tartrate- (TAT) selective electrode has been developed for determination of tartaric acid in wines. Several electrodes constructed for this purpose had a PVC membrane with a complex of quaternary ammonium and TAT as anion exchanger, a phenol derivative as additive, and a more or less polar mediator solvent. Characterization of the electrodes showed behavior was best for membranes with o-nitrophenyl octyl ether as solvent. On injection of 500 μL into a phosphate buffer carrier (pH = 3.1; ionic strength 10–2 mol/L) flowing at 3 mL/min, the slope was 58.06 ± 0.6 with a lower limit of linear range of 5.0 × 10–4 mol/L TAT and R2 = 0.9989. The interference of several species, e.g. chloride, bromide, iodide, nitrate, gallic acid, tannin, sucrose, glucose, fructose, acetate, and citrate, was evaluated in terms of potentiometric selectivity coefficients. The Hofmeister series was followed for inorganic species and the most interfering organic ion was citrate. When red and white wines were analyzed and the results compared with those from an independent method they were found to be accurate, with relative standard deviations below 5.0%.

Diane Arbus: the wonderful wizard of odds or the poetics of the i (eye)

Diane Arbus‘ photographs are mainly about difference. Most of the time she is trying ‗[…] to suppress, or at least reduce, moral and sensory queasiness‘ (Sontag 1977: 40) in order to represent a world where the subject of the photograph is not merely the ‗other‘ but also the I. Her technique does not coax her subjects into natural poses. Instead she encourages them to be strange and awkward. By posing for her, the revelation of the self is identified with what is odd. This paper aims at understanding the geography of difference that, at the same time, is also of resistance, since Diane Arbus reveals what was forcefully hidden by bringing it into light in such a way that it is impossible to ignore. Her photographs display a poetic beauty that is not only of the ‗I‘ but also of the ‗eye‘. The world that is depicted is one in which we are all the same. She ―atomizes‖ reality by separating each element and ‗Instead of showing identity between things which are different […] everybody is shown to look the same.‘ (Sontag 1977: 47). Furthermore, this paper analyses some of Arbus‘ photographs so as to explain this point of view, by trying to argue that between rejecting and reacting against what is standardized she does not forget the geography of the body which is also a geography of the self. While creating a new imagetic topos, where what is trivial becomes divine, she also presents the frailty of others as our own.

To Ada or not To Ada: Adaing vs. Javaing in real-time systems

Ada is really an unfortunate Lady. After years fighting against C/C++ villains, her major lift-up (Ada 95) had brought up a promise of fortune. However, a new strong villain (Java) has appeared trying to end her struggle for survival. Ada has now to fight with her own weapons. She will only prosper by her own merits. But two questions emerge. Do they exist? Are they better than Java’s? Our opinion is that they do exist, and are not matched by any other programming language

Slow down or race to halt: towards managing complexity of real-time energy management decisions

Existing work in the context of energy management for real-time systems often ignores the substantial cost of making DVFS and sleep state decisions in terms of time and energy and/or assume very simple models. Within this paper we attempt to explore the parameter space for such decisions and possible constraints faced.