Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

Determination of sorbate and benzoate in beverage samples by capillary electrophoresis - Optimization of the method with inspection of ionic mobilities

The aim of this study was to develop a fast capillary electrophoresis method for the determination of benzoate and sorbate ions in commercial beverages. In the method development the pH and constituents of the background electrolyte were selected using the effective mobility versus pH curves. As the high resolution obtained experimentally for sorbate and benzoate in the studies presented in the literature is not in agreement with that expected from the ionic mobility values published, a procedure to determine these values was carried out. The salicylate ion was used as the internal standard. The background electrolyte was composed of 25 mmol L(-1) tris(hydroxymethyl)aminomethane and 12.5 mmol L(-1) 2-hydroxyisobutyric acid, atpH 8.1.Separation was conducted in a fused-silica capillary(32 cm total length and 8.5 cm effective length, 50 mu m I.D.), with short-end injection configuration and direct UV detection at 200 nm for benzoate and salicylate and 254 nm for sorbate ions. The run time was only 28 s. A few figures of merit of the proposed method include: good linearity (R(2) > 0.999), limit of detection of 0.9 and 0.3 mg L(-1) for benzoate and sorbate, respectively, inter-day precision better than 2.7% (n =9) and recovery in the range 97.9-105%. Beverage samples were prepared by simple dilution with deionized water (1:11, v/v). Concentrations in the range of 197-401 mg L(-1) for benzoate and 28-144 mg L(-1) for sorbate were found in soft drinks and tea. (c) 2008 Elsevier B.V. All rights reserved.

A new and improved strategy combining a dispersive-solid phase extraction-based multiclass method with ultra high pressure liquid chromatography for analysis of low molecular weight polyphenols in vegetables

This paper reports on the development and optimization of a modified Quick, Easy, Cheap Effective, Rugged and Safe (QuEChERS) based extraction technique coupled with a clean-up dispersive-solid phase extraction (dSPE) as a new, reliable and powerful strategy to enhance the extraction efficiency of free low molecular-weight polyphenols in selected species of dietary vegetables. The process involves two simple steps. First, the homogenized samples are extracted and partitioned using an organic solvent and salt solution. Then, the supernatant is further extracted and cleaned using a dSPE technique. Final clear extracts of vegetables were concentrated under vacuum to near dryness and taken up into initial mobile phase (0.1% formic acid and 20% methanol). The separation and quantification of free low molecular weight polyphenols from the vegetable extracts was achieved by ultrahigh pressure liquid chromatography (UHPLC) equipped with a phodiode array (PDA) detection system and a Trifunctional High Strength Silica capillary analytical column (HSS T3), specially designed for polar compounds. The performance of the method was assessed by studying the selectivity, linear dynamic range, the limit of detection (LOD) and limit of quantification (LOQ), precision, trueness, and matrix effects. The validation parameters of the method showed satisfactory figures of merit. Good linearity (View the MathML sourceRvalues2>0.954; (+)-catechin in carrot samples) was achieved at the studied concentration range. Reproducibility was better than 3%. Consistent recoveries of polyphenols ranging from 78.4 to 99.9% were observed when all target vegetable samples were spiked at two concentration levels, with relative standard deviations (RSDs, n = 5) lower than 2.9%. The LODs and the LOQs ranged from 0.005 μg mL−1 (trans-resveratrol, carrot) to 0.62 μg mL−1 (syringic acid, garlic) and from 0.016 μg mL−1 (trans-resveratrol, carrot) to 0.87 μg mL−1 ((+)-catechin, carrot) depending on the compound. The method was applied for studying the occurrence of free low molecular weight polyphenols in eight selected dietary vegetables (broccoli, tomato, carrot, garlic, onion, red pepper, green pepper and beetroot), providing a valuable and promising tool for food quality evaluation.

Curves in homogeneous spaces and their contact with 1-dimensional orbits

Let alpha be a C(infinity) curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace S(k)(alpha) of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose orbit through x has contact of order k with alpha. In this paper, we give various important properties of the sequence of subspaces G superset of S(1)(alpha) superset of S(2)(alpha) superset of S(3)(alpha) superset of ... In particular, we give a stabilization property for certain well-behaved curves. We also describe its relationship to the isotropy subgroup with respect to the contact element of order k associated with alpha.

Influence of Tapered and External Hexagon Connections on Bone Stresses Around Tilted Dental Implants: Three-Dimensional Finite Element Method With Statistical Analysis

Background: The purpose of this study is to analyze the tension distribution on bone tissue around implants with different angulations (0 degrees, 17 degrees, and 30 degrees) and connections (external hexagon and tapered) through the use of three-dimensional finite element and statistical analyses.Methods: Twelve different configurations of three-dimensional finite element models, including three inclinations of the implants (0 degrees, 17 degrees, and 30 degrees), two connections (an external hexagon and a tapered), and two load applications (axial and oblique), were simulated. The maximum principal stress values for cortical bone were measured at the mesial, distal, buccal, and lingual regions around the implant for each analyzed situation, totaling 48 groups. Loads of 200 and 100 N were applied at the occlusal surface in the axial and oblique directions, respectively. Maximum principal stress values were measured at the bone crest and statistically analyzed using analysis of variance. Stress patterns in the bone tissue around the implant were analyzed qualitatively.Results: The results demonstrated that under the oblique loading process, the external hexagon connection showed significantly higher stress concentrations in the bone tissue (P < 0.05) compared with the tapered connection. Moreover, the buccal and mesial regions of the cortical bone concentrated significantly higher stress (P < 0.005) to the external hexagon implant type. Under the oblique loading direction, the increased external hexagon implant angulation induced a significantly higher stress concentration (P = 0.045).Conclusions: The study results show that: 1) the oblique load was more damaging to bone tissue, mainly when associated with external hexagon implants; and 2) there was a higher stress concentration on the buccal region in comparison to all other regions under oblique load.

Validation of a stability-indicating HPLC method with diode array detection for the determination of beclomethasone dipropionate in aqueous suspension for nebulizer

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems.

Application of active heat pulse method with fiber optic temperature sensing for estimation of wetting bulbs and water distribution in drip emitters.

Through the use of the Distributed Fiber Optic Temperature Measurement (DFOT) method, it is possible to measure the temperature in small intervals (on the order of centimeters) for long distances (on the order of kilometers) with a high temporal frequency and great accuracy. The heat pulse method consists of applying a known amount of heat to the soil and monitoring the temperature evolution, which is primarily dependent on the soil moisture content. The use of both methods, which is called the active heat pulse method with fiber optic temperature sensing (AHFO), allows accurate soil moisture content measurements. In order to experimentally study the wetting patterns, i.e. shape, size, and the water distribution, from a drip irrigation emitter, a soil column of 0.5 m of diameter and 0.6 m high was built. Inside the column, a fiber optic cable with a stainless steel sheath was placed forming three concentric helixes of diameters 0.2 m, 0.4 m and 0.6 m, leading to a 148 measurement point network. Before, during, and after the irrigation event, heat pulses were performed supplying electrical power of 20 W/m to the steel. The soil moisture content was measured with a capacitive sensor in one location at depths of 0.1 m, 0.2 m, 0.3 m and 0.4 m during the irrigation. It was also determined by the gravimetric method in several locations and depths before and right after the irrigation. The emitter bulb dimensions and shape evolution was satisfactorily measured during infiltration. Furthermore, some bulb's characteristics difficult to predict (e.g. preferential flow) were detected. The results point out that the AHFO is a useful tool to estimate the wetting pattern of drip irrigation emitters in soil columns and show a high potential for its use in the field.

A linearization-based system reliability method with application to geotechnical analysis

Los análisis de fiabilidad representan una herramienta adecuada para contemplar las incertidumbres inherentes que existen en los parámetros geotécnicos. En esta Tesis Doctoral se desarrolla una metodología basada en una linealización sencilla, que emplea aproximaciones de primer o segundo orden, para evaluar eficientemente la fiabilidad del sistema en los problemas geotécnicos. En primer lugar, se emplean diferentes métodos para analizar la fiabilidad de dos aspectos propios del diseño de los túneles: la estabilidad del frente y el comportamiento del sostenimiento. Se aplican varias metodologías de fiabilidad — el Método de Fiabilidad de Primer Orden (FORM), el Método de Fiabilidad de Segundo Orden (SORM) y el Muestreo por Importancia (IS). Los resultados muestran que los tipos de distribución y las estructuras de correlación consideradas para todas las variables aleatorias tienen una influencia significativa en los resultados de fiabilidad, lo cual remarca la importancia de una adecuada caracterización de las incertidumbres geotécnicas en las aplicaciones prácticas. Los resultados también muestran que tanto el FORM como el SORM pueden emplearse para estimar la fiabilidad del sostenimiento de un túnel y que el SORM puede mejorar el FORM con un esfuerzo computacional adicional aceptable. Posteriormente, se desarrolla una metodología de linealización para evaluar la fiabilidad del sistema en los problemas geotécnicos. Esta metodología solamente necesita la información proporcionada por el FORM: el vector de índices de fiabilidad de las funciones de estado límite (LSFs) que componen el sistema y su matriz de correlación. Se analizan dos problemas geotécnicos comunes —la estabilidad de un talud en un suelo estratificado y un túnel circular excavado en roca— para demostrar la sencillez, precisión y eficiencia del procedimiento propuesto. Asimismo, se reflejan las ventajas de la metodología de linealización con respecto a las herramientas computacionales alternativas. Igualmente se muestra que, en el caso de que resulte necesario, se puede emplear el SORM —que aproxima la verdadera LSF mejor que el FORM— para calcular estimaciones más precisas de la fiabilidad del sistema. Finalmente, se presenta una nueva metodología que emplea Algoritmos Genéticos para identificar, de manera precisa, las superficies de deslizamiento representativas (RSSs) de taludes en suelos estratificados, las cuales se emplean posteriormente para estimar la fiabilidad del sistema, empleando la metodología de linealización propuesta. Se adoptan tres taludes en suelos estratificados característicos para demostrar la eficiencia, precisión y robustez del procedimiento propuesto y se discuten las ventajas del mismo con respecto a otros métodos alternativos. Los resultados muestran que la metodología propuesta da estimaciones de fiabilidad que mejoran los resultados previamente publicados, enfatizando la importancia de hallar buenas RSSs —y, especialmente, adecuadas (desde un punto de vista probabilístico) superficies de deslizamiento críticas que podrían ser no-circulares— para obtener estimaciones acertadas de la fiabilidad de taludes en suelos. Reliability analyses provide an adequate tool to consider the inherent uncertainties that exist in geotechnical parameters. This dissertation develops a simple linearization-based approach, that uses first or second order approximations, to efficiently evaluate the system reliability of geotechnical problems. First, reliability methods are employed to analyze the reliability of two tunnel design aspects: face stability and performance of support systems. Several reliability approaches —the first order reliability method (FORM), the second order reliability method (SORM), the response surface method (RSM) and importance sampling (IS)— are employed, with results showing that the assumed distribution types and correlation structures for all random variables have a significant effect on the reliability results. This emphasizes the importance of an adequate characterization of geotechnical uncertainties for practical applications. Results also show that both FORM and SORM can be used to estimate the reliability of tunnel-support systems; and that SORM can outperform FORM with an acceptable additional computational effort. A linearization approach is then developed to evaluate the system reliability of series geotechnical problems. The approach only needs information provided by FORM: the vector of reliability indices of the limit state functions (LSFs) composing the system, and their correlation matrix. Two common geotechnical problems —the stability of a slope in layered soil and a circular tunnel in rock— are employed to demonstrate the simplicity, accuracy and efficiency of the suggested procedure. Advantages of the linearization approach with respect to alternative computational tools are discussed. It is also found that, if necessary, SORM —that approximates the true LSF better than FORM— can be employed to compute better estimations of the system’s reliability. Finally, a new approach using Genetic Algorithms (GAs) is presented to identify the fully specified representative slip surfaces (RSSs) of layered soil slopes, and such RSSs are then employed to estimate the system reliability of slopes, using our proposed linearization approach. Three typical benchmark-slopes with layered soils are adopted to demonstrate the efficiency, accuracy and robustness of the suggested procedure, and advantages of the proposed method with respect to alternative methods are discussed. Results show that the proposed approach provides reliability estimates that improve previously published results, emphasizing the importance of finding good RSSs —and, especially, good (probabilistic) critical slip surfaces that might be non-circular— to obtain good estimations of the reliability of soil slope systems.

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

A Component Based Heuristic Search Method with AdaptivePerturbations for Hospital Personnel Scheduling

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with adaptive perturbations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then mimic a natural evolutionary process on these components to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs a dynamic evaluation function which evaluates how well each component contributes towards the final objective. Two perturbation steps are then applied: the first perturbation eliminates a number of components that are deemed not worthy to stay in the current schedule; the second perturbation may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

A meshfree-based local Galerkin method with condensation of degree of freedom

Condensation technique of degree of freedom is firstly proposed to improve the computational efficiency of meshfree method with Galerkin weak form. In present method, scattered nodes without connectivity are divided into several subsets by cells with arbitrary shape. The local discrete equations are established over each cell by using moving kriging interpolation, in which the nodes that located in the cell are used for approximation. Then, the condensation technique can be introduced into the local discrete equations by transferring equations of inner nodes to equations of boundary nodes based on cell. In the scheme of present method, the calculation of each cell is carried out by meshfree method with Galerkin weak form, and local search is implemented in interpolation. Numerical examples show that the present method has high computational efficiency and convergence, and good accuracy is also obtained.