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/.

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Evaluating bound-constrained minimization software

Bound-constrained minimization is a subject of active research. To assess the performance of existent solvers, numerical evaluations and comparisons are carried on. Arbitrary decisions that may have a crucial effect on the conclusions of numerical experiments are highlighted in the present work. As a result, a detailed evaluation based on performance profiles is applied to the comparison of bound-constrained minimization solvers. Extensive numerical results are presented and analyzed.

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.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

Análise dos erros na estimação de gradientes em malhas de Voronoi

Este trabalho apresenta um estudo teórico e numérico sobre os erros que ocorrem nos cálculos de gradientes em malhas não estruturadas constituídas pelo diagrama de Voronoi, malhas estas, formadas também pela triangulação de Delaunay. As malhas adotadas, no trabalho, foram as malhas cartesianas e as malhas triangulares, esta última é gerada pela divisão de um quadrado em dois ou quatro triângulos iguais. Para tal análise, adotamos a escolha de três metodologias distintas para o cálculo dos gradientes: método de Green Gauss, método do Mínimo Resíduo Quadrático e método da Média do Gradiente Projetado Corrigido. O texto se baseia em dois enfoques principais: mostrar que as equações de erros dadas pelos gradientes podem ser semelhantes, porém com sinais opostos, para pontos de cálculos em volumes vizinhos e que a ordem do erro das equações analíticas pode ser melhorada em malhas uniformes quando comparada as não uniformes, nos casos unidimensionais, e quando analisada na face de tais volumes vizinhos nos casos bidimensionais.

Spectral zero-crossings: localization properties and application to epoch extraction in speech signals

We analyze the spectral zero-crossing rate (SZCR) properties of transient signals and show that SZCR contains accurate localization information about the transient. For a train of pulses containing transient events, the SZCR computed on a sliding window basis is useful in locating the impulse locations accurately. We present the properties of SZCR on standard stylized signal models and then show how it may be used to estimate the epochs in speech signals. We also present comparisons with some state-of-the-art techniques that are based on the group-delay function. Experiments on real speech show that the proposed SZCR technique is better than other group-delay-based epoch detectors. In the presence of noise, a comparison with the zero-frequency filtering technique (ZFF) and Dynamic programming projected Phase-Slope Algorithm (DYPSA) showed that performance of the SZCR technique is better than DYPSA and inferior to that of ZFF. For highpass-filtered speech, where ZFF performance suffers drastically, the identification rates of SZCR are better than those of DYPSA.

William Herschel Telescope observations of distant comets

We present results from broad-band V- and R-filter observations obtained at the 4.2-m William Herschel Telescope on La Palma on 2002 July 12-14. A total of six comets were imaged, and their heliocentric distances ranged from 2.8 to 6.1 au. The comets observed were 43P/Wolf-Harrington, 129P/Shoemaker-Levy 3, 133P/Elst-Pizarro, 143P/Kowal-Mrkos, P/1998 U4 (Spahr) and P/2001 H5 (NEAT). A detailed surface brightness profile analysis indicates that three of the targeted comets (43P/Wolf-Harrington, 129P/Shoemaker-Levy 3 and P/1998 U4) were visibly active, and the remaining three comets were stellar in appearance. Further analysis shows that for the three `stellar-like' comets the possible coma contribution to the observed flux does not exceed 12.2 per cent, and in the case of comet 143P/Kowal-Mrkos the coma contribution is expected to be as low as 1 per cent, and so the resulting photometry most likely represents that of the projected nucleus surface. Effective radii for the inactive comets range from 1.02 to 4.56 km, and the effective radius upper limits for the active comets range from 1.94 to 4.15 km. We assume an albedo and phase coefficient of 0.04 and 0.035 mag deg-1, respectively, with the exception of comets 133P/Elst-Pizarro and 143P/Kowal-Mrkos for which phase coefficients were previously measured. These values are compared with previous measurements, and for comet 43P/Wolf-Harrington we find that the nucleus axial ratio a/b could be as large as 2.44. For the active comets we measured dust production levels in terms of the Af? quantity. Spectral gradients were extracted for two of the inactive comets from their measured broad-band colour indices, and compared with the rest of the comet population for which (V-R) colour and spectral gradient values exist. We find a spectral gradient for 143P/Kowal-Mrkos of 9.9 +/- 8.1 per cent/100 nm, which is very typical of Jupiter-family comets, the majority of which have reflectivity gradients in the range 0-13 per cent (100 nm)-1. The spectral gradient for comet 133P/Elst-Pizarro is amongst the bluest yet measured. We measure a (V-R) colour index value of 0.14 +/- 0.11 for the nucleus of 133P/Elst-Pizarro which is considerably lower than previous measurements. A possible explanation for this difference is considered.

Blue luminous stars in nearby galaxies: Quantitative spectral analysis of M33 B-type supergiant stars

We present the detailed spectral analysis of a sample of M33 B-type supergiant stars, aimed at the determination of their fundamental parameters and chemical composition. The analysis is based on a grid of non-LTE metal line-blanketed model atmospheres including the effects of stellar winds and spherical extension computed with the code FASTWIND. Surface abundance ratios of C, N, and O are used to discuss the chemical evolutionary status of each individual star. The comparison of observed stellar properties with theoretical predictions of massive star evolutionary models shows good agreement within the uncertainties of the analysis. The spatial distribution of the sample allows us to investigate the existence of radial abundance gradients in the disk of M33. The comparison of stellar and H II region O abundances ( based on direct determinations of the electron temperature of the nebulae) shows good agreement. Using a simple linear radial representation, the stellar oxygen abundances result in a gradient of -0.0145 +/- 0.005 dex arcmin(-1) (or -0.06 +/- 0.02 dex kpc(-1)) up to a distance equal to similar to 1.1 times the isophotal radius of the galaxy. A more complex representation cannot be completely discarded by our stellar sample. The stellar Mg and Si abundances follow the trend displayed by O abundances, although with shallower gradients. These differences in gradient slope cannot be explained at this point. The derived abundances of the three alpha-elements yield solar metallicity in the central regions of the disk of M33. A comparison with recent planetary nebula data from Magrini and coworkers indicates that the disk of M33 has not suffered from a significant O enrichment in the last 3 Gyr.

hyDRaCAT Spectral Reflectance Library: Hyperspectral Field Spectroscopy and Field Spectro-Goniometry of Siberian and Alaskan Tundra

hyDRaCAT Spectral Reflectance Library for tundra provides the surface reflectance data and the bidirectional reflectance distribution function (BRDF) of important Arctic tundra vegetation communities at representative Siberian and Alaskan tundra sites. The aim of this dataset is the hyperspectral and spectro-directional reflectance characterization as basis for the extraction of vegetation parameters, and the normalization of BRDF effects in off-nadir and multi-temporal remote sensing data. The spectroscopic and field spectro-goniometric measurements were undertaken on the YAMAL2011 expedition of representative Siberian vegetation fields and on the North American Arctic Transect NAAT2012 expedition of Alaskan vegetation fields both belonging to the Greening-of-the-Arctic (GOA) program. For the field spectroscopy each 100 m2 vegetation study grid was divided into quadrats of 1 × 1 m. The averaged reflectance of all quadrats represents the spectral reflectance at the scale of the whole grid at the 10 × 10 m scale. For the surface radiometric measurements two GER1500 portable field spectroradiometers (Spectra Vista Corporation, Poughkeepsie, NY, USA) were used. The GER1500 measures radiance across the wavelength range of 350-1,050 nm, with sampling intervals of 1.5 nm and a radiance accuracy of 1.2 × 10**-1 W/cm**2/nm/sr. In order to increase the signal-to-noise ratio, 32 individual measurements were averaged per one target scan. To minimize variations in the target reflectance due to sun zenith angle changes, all measurements at one study location have been performed under similar sun zenith angles and during clear-sky conditions. The field spectrometer measurements were carried out with a GER1500 UV-VIS spectrometer The spectrogoniometer measurements were carried out with a self-designed spectro-goniometer: the Manual Transportable Instrument platform for ground-based Spectro-directional observations (ManTIS, patent publication number: DE 10 2011 117 713.A1). The ManTIS was equipped with the GER1500 spectrometer allowing spectro-directional measurements with up to 30° viewing zenith angle by full 360° viewing azimuth angles. Measurements in central Yamal (Siberia) at the research site 'Vaskiny Dachi' were carried out in the late summer phenological state from August 12 2011 to August 28 2011. All measurements in Alaska along the North South transect on the North Slope were taken between 29 June and 11 July 2012, ensuring that the vegetation was in the same phenological state near peak growing season.