Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

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.

Optimizing potentiometric ionophore and electrode design for environmental on-site control of antibiotic drugs: Application to sulfamethoxazole

Potentiometric sensors are typically unable to carry out on-site monitoring of environmental drug contaminants because of their high limits of detection (LODs). Designing a novel ligand material for the target analyte and managing the composition of the internal reference solution have been the strategies employed here to produce for the first time a potentiometric-based direct reading method for an environmental drug contaminant. This concept has been applied to sulfamethoxazole (SMX), one of the many antibiotics used in aquaculture practices that may occur in environmental waters. The novel ligand has been produced by imprinting SMX on the surface of graphitic carbon nanostructures (CN) < 500 nm. The imprinted carbon nanostructures (ICN) were dispersed in plasticizer and entrapped in a PVC matrix that included (or not) a small amount of a lipophilic additive. The membrane composition was optimized on solid-contact electrodes, allowing near-Nernstian responses down to 5.2 μg/mL and detecting 1.6 μg/mL. The membranes offered good selectivity against most of the ionic compounds in environmental water. The best membrane cocktail was applied on the smaller end of a 1000 μL micropipette tip made of polypropylene. The tip was then filled with inner reference solution containing SMX and chlorate (as interfering compound). The corresponding concentrations were studied for 1 × 10−5 to 1 × 10−10 and 1 × 10−3 to 1 × 10−8 mol/L. The best condition allowed the detection of 5.92 ng/L (or 2.3 × 10−8 mol/L) SMX for a sub-Nernstian slope of −40.3 mV/decade from 5.0 × 10−8 to 2.4 × 10−5 mol/L.

Ensino direto da matemática funcional: estudo de caso

Neste estudo, focado na aprendizagem do manuseio do dinheiro, pretendeu-se que os alunos adquirissem competências que os habilitasse a um maior grau de independência e participação na vida em sociedade, desempenhando tarefas de cariz financeiro de forma mais independente, por exemplo, compra de produtos, pagamento de serviços e gestão do dinheiro. Para alcançar o pretendido, utilizou-se a metodologia do ensino direto, com tarefas estruturadas. Numa fase inicial o investigador prestava apoio constante aos alunos, que foi diminuindo gradualmente à medida que atingiam as competências relacionadas com o dinheiro. Na fase final, os alunos realizaram as tarefas propostas de forma autónoma. Construído como um estudo de caso, os dados foram recolhidos através de observação direta e de provas de monitorização. Os alunos começaram por realizar uma avaliação inicial para delinear a linha de base da intervenção. Posteriormente, foi realizada a intervenção baseada no ensino direto, com recurso ao computador, à calculadora, a provas de monitorização e ao manuseio de dinheiro. O computador foi utilizado na intervenção como tecnologia de apoio à aprendizagem, permitindo a realização de jogos interativos e consulta de materiais. No final da intervenção os alunos revelaram autonomia na resolução das tarefas, pois já tinham automatizado os processos matemáticas para saber manusear corretamente a moeda euro. O ensino direto auxiliou os alunos a reterem as competências matemáticas essenciais de manuseamento do dinheiro, compondo quantias, efetuando pagamentos e conferindo trocos, que muito podem contribuir para terem uma participação independente na vida em sociedade

Fast screening procedure for antibiotics in wastewaters by direct HPLC-DAD analysis

Growing concern about the contamination of wastewaters by antibiotics demands fast but sensitive analytical methodologies, for the screening of a large number of samples. The purpose of this work was to develop a simple methodology, using direct injection of the samples, by HPLC with diode array detection (DAD), for a multiresidue analysis of five antibiotics of different classes. Wastewater from an urban water treatment plant was selected as a model to study possible coelution of interfering compounds. The linearity interval ranged from 40 to 400 µg/L for amoxicillin (Amox), metronidazole (Metro), cefazolin (Cefa), and chloramphenicol (Chloram) and from 20 to 200 µg/L for sulfamethoxazole (Sulfa), with LODs lower than 14 µg/L. Repeatability, expressed by the CV of six repeated injections, ranged from 1 to 8%, while the intermediate precision varied between 2 and 11%. The recovery ranged from 90 to 109%. This method enables the fast screening of a large number of samples, with an expanded uncertainty in the 1–22% range. The advantage of the proposed method is to significantly reduce the number of samples to be analyzed by more complex methods.

Direct electroanalytical determination of fluvastatin in a pharmaceutical dosage form: batch and flow analysis

The reduction of luvastatin (FLV) at a hanging mercury-drop electrode (HMDE) was studied by square-wave adsorptive-stripping voltammetry (SWAdSV). FLV can be accumulated and reduced at the electrode, with a maximum peak current intensity at a potential of approximately 1.26V vs. AgCl=Ag, in an aqueous electrolyte solution of pH 5.25. The method shows linearity between peak current intensity and FLV concentration between 1.0 10 8 and 2.7 10 6 mol L 1. Limits of detection (LOD) and quantification (LOQ) were found to be 9.9 10 9 mol L 1 and 3.3 10 8 mol L 1, respectively. Furthermore, FLV oxidation at a glassy carbon electrode surface was used for its hydrodynamic monitoring by amperometric detection in a flow-injection system. The amperometric signal was linear with FLV concentration over the range 1.0 10 6 to 1.0 10 5 mol L 1, with an LOD of 2.4 10 7 mol L 1 and an LOQ of 8.0 10 7 mol L 1. A sample rate of 50 injections per hour was achieved. Both methods were validated and showed to be precise and accurate, being satisfactorily applied to the determination of FLV in a commercial pharmaceutical.

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.