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/.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

NMR Chemical Shielding and Spin-Spin Coupling Constants of Liquid NH(3): A Systematic Investigation using the Sequential QM/MM Method

The NMR spin coupling parameters, (1)J(N,H) and (2)J(H,H), and the chemical shielding, sigma((15)N), of liquid ammonia are studied from a combined and sequential QM/MM methodology. Monte Carlo simulations are performed to generate statistically uncorrelated configurations that are submitted to density functional theory calculations. Two different Lennard-Jones potentials are used in the liquid simulations. Electronic polarization is included in these two potentials via an iterative procedure with and without geometry relaxation, and the influence on the calculated properties are analyzed. B3LYP/aug-cc-pVTZ-J calculations were used to compute the V(N,H) constants in the interval of -67.8 to -63.9 Hz, depending on the theoretical model used. These can be compared with the experimental results of -61.6 Hz. For the (2)J(H,H) coupling the theoretical results vary between -10.6 to -13.01 Hz. The indirect experimental result derived from partially deuterated liquid is -11.1 Hz. Inclusion of explicit hydrogen bonded molecules gives a small but important contribution. The vapor-to-liquid shifts are also considered. This shift is calculated to be negligible for (1)J(N,H) in agreement with experiment. This is rationalized as a cancellation of the geometry relaxation and pure solvent effects. For the chemical shielding, U(15 N) Calculations at the B3LYP/aug-pcS-3 show that the vapor-to-liquid chemical shift requires the explicit use of solvent molecules. Considering only one ammonia molecule in an electrostatic embedding gives a wrong sign for the chemical shift that is corrected only with the use of explicit additional molecules. The best result calculated for the vapor to liquid chemical shift Delta sigma((15)N) is -25.2 ppm, in good agreement with the experimental value of -22.6 ppm.

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.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Integrated marine gravity field in the Brazilian coast from altimeter-derived sea surface gradient and shipborne gravity

Sea surface gradients derived from the Geosat and ERS-1 satellite altimetry geodetic missions were integrated with marine gravity data from the National Geophysical Data Center and Brazilian national surveys. Using the least squares collocation method, models of free-air gravity anomaly and geoid height were calculated for the coast of Brazil with a resolution of 2` x 2`. The integration of satellite and shipborne data showed better statistical results in regions near the coast than using satellite data only, suggesting an improvement when compared to the state-of-the-art global gravity models. Furthermore, these results were obtained with considerably less input information than was used by those reference models. The least squares collocation presented a very low content of high-frequency noise in the predicted gravity anomalies. This may be considered essential to improve the high resolution representation of the gravity field in regions of ocean-continent transition. (C) 2010 Elsevier Ltd. All rights reserved.

The genetic effects of Late Quaternary climatic changes over a tropical latitudinal gradient: diversification of an Atlantic Forest passerine

The increase in biodiversity from high to low latitudes is a widely recognized biogeographical pattern. According to the latitudinal gradient hypothesis (LGH), this pattern was shaped by differential effects of Late Quaternary climatic changes across a latitudinal gradient. Here, we evaluate the effects of climatic changes across a tropical latitudinal gradient and its implications to diversification of an Atlantic Forest (AF) endemic passerine. We studied the intraspecific diversification and historical demography of Sclerurus scansor, based on mitochondrial (ND2, ND3 and cytb) and nuclear (FIB7) gene sequences. Phylogenetic analyses recovered three well-supported clades associated with distinct latitudinal zones. Coalescent-based methods were applied to estimate divergence times and changes in effective population sizes. Estimates of divergence times indicate that intraspecific diversification took place during Middle-Late Pleistocene. Distinct demographic scenarios were identified, with the southern lineage exhibiting a clear signature of demographic expansion, while the central one remained more stable. The northern lineage, contrasting with LGH predictions, exhibited a clear sign of a recent bottleneck. Our results suggest that different AF regions reacted distinctly, even in opposite ways, under the same climatic period, producing simultaneously favourable scenarios for isolation and contact among populations.

Role of Surfactants in Carbon Nanotubes Density Gradient Separation

Several strategies aimed at sorting single-walled carbon nanotubes (SWNT) by diameter and/or electronic structure have been developed in recent years. A nondestructive sorting method was recently proposed in which nanotube bundles are dispersed in water-surfactant solutions and submitted to ultracentrifugation in a density gradient. By this method, SWNTs of different diameters are distributed according to their densities along the centrifuge tube. A mixture of two anionic amphiphiles, namely sodium dodecylsulfate (SIDS) and sodium cholate (SC), presented the best performance in discriminating nanotubes by diameter. We present molecular dynamics studies of the water-surfactant-SWNT system. The simulations revealed one aspect of the discriminating power of surfactants: they can actually be attracted toward the interior of the nanotube cage. The binding energies of SDS and SC on the outer nanotube surface are very similar and depend weakly on diameter. The binding inside the tubes, on the contrary, is strongly diameter dependent: SDS fits best inside tubes with diameters ranging from 8 to 9 angstrom, while SC is best accommodated in larger tubes, with diameters in the range 10.5-12 angstrom. The dynamics at room temperature showed that, as the amphiphile moves to the hollow cage, water molecules are dragged together, thereby promoting the nanotube filling. The resulting densities of filled SWNT are in agreement with measured densities.

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

A method for Ca, Fe, Ga, Na, Si and Zn determination in alumina by inductively coupled plasma optical emission spectrometry after aluminum precipitation

In this present work a method for the determination of Ca, Fe, Ga, Na, Si and Zn in alumina (Al(2)O(3)) by inductively coupled plasma optical emission spectrometry (ICP OES) with axial viewing is presented. Preliminary studies revealed intense aluminum spectral interference over the majority of elements and reaction between aluminum and quartz to form aluminosilicate, reducing drastically the lifetime of the torch. To overcome these problems alumina samples (250 mg) were dissolved with 5 mL HCl + 1.5 mLH(2)SO(4) + 1.5 mL H(2)O in a microwave oven. After complete dissolution the volume was completed to 20 mL and aluminum was precipitated as Al(OH)(3) with NH(3) (by bubbling NH(3) into the solution up to a pH similar to 8, for 10 min). The use of internal standards (Fe/Be, Ga/Dy, Zn/In and Na/Sc) was essential to obtain precise and accurate results. The reliability of the proposed method was checked by analysis of alumina certified reference material (Alumina Reduction Grade-699, NIST). The found concentrations (0.037%w(-1) CaO, 0.013% w w(-1) Fe(2)O(3), 0.012%w w(-1)Ga(2)O(3), 0.49% w w(-1) Na(2)O, 0.014% w w(-1) SiO(2) and 0.013% w w(-1) ZnO) presented no statistical differences compared to the certified values at a 95% confidence level. (C) 2011 Elsevier B.V. All rights reserved.