Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

Uma adaptação do método barreira penalidade quasi-Newton ao problema de fluxo de potência ótimo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

Inter- and intralaboratory variation of in vitro diffusion cell measurements: An international multicenter study using quasi-standardized methods and materials

In vitro measurements of skin absorption are an increasingly important aspect of regulatory studies, product support claims, and formulation screening. However, such measurements are significantly affected by skin variability. The purpose of this study was to determine inter- and intralaboratory variation in diffusion cell measurements caused by factors other than skin. This was attained through the use of an artificial (silicone rubber) rate-limiting membrane and the provision of materials including a standard penetrant, methyl paraben (MP), and a minimally prescriptive protocol to each of the 18 participating laboratories. Standardized calculations of MP flux were determined from the data submitted by each laboratory by applying a predefined mathematical model. This was deemed necessary to eliminate any interlaboratory variation caused by different methods of flux calculations. Average fluxes of MP calculated and reported by each laboratory (60 +/- 27 mug cm(-2) h(-1), n = 25, range 27-101) were in agreement with the standardized calculations of MP flux (60 +/- 21 mug cm(-2) h(-1), range 19-120). The coefficient of variation between laboratories was approximately 35% and was manifest as a fourfold difference between the lowest and highest average flux values and a sixfold difference between the lowest and highest individual flux values. Intra-laboratory variation was lower, averaging 10% for five individuals using the same equipment within a single laboratory. Further studies should be performed to clarify the exact components responsible for nonskin-related variability in diffusion cell measurements. It is clear that further developments of in vitro methodologies for measuring skin absorption are required. (C) 2005 Wiley-Liss, Inc.

Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

AMS Subj. Classification: 49J15, 49M15

New contributions to the determination of resonance frequencies of rectangular microstrip antennas by neural networks

This paper uses artificial neural networks (ANN) to compute the resonance frequencies of rectangular microstrip antennas (MSA), used in mobile communications. Perceptron Multi-layers (PML) networks were used, with the Quasi-Newton method proposed by Broyden, Fletcher, Goldfarb and Shanno (BFGS). Due to the nature of the problem, two hundred and fifty networks were trained, and the resonance frequency for each test antenna was calculated by statistical methods. The estimate resonance frequencies for six test antennas were compared with others results obtained by deterministic and ANN based empirical models from the literature, and presented a better agreement with the experimental values.

A simple analysis of the influence of the solvent-induced electronic polarization on the N-15 magnetic shielding of pyridine in water

Electronic polarization induced by the interaction of a reference molecule with a liquid environment is expected to affect the magnetic shielding constants. Understanding this effect using realistic theoretical models is important for proper use of nuclear magnetic resonance in molecular characterization. In this work, we consider the pyridine molecule in water as a model system to briefly investigate this aspect. Thus, Monte Carlo simulations and quantum mechanics calculations based on the B3LYP/6-311++G (d,p) are used to analyze different aspects of the solvent effects on the N-15 magnetic shielding constant of pyridine in water. This includes in special the geometry relaxation and the electronic polarization of the solute by the solvent. The polarization effect is found to be very important, but, as expected for pyridine, the geometry relaxation contribution is essentially negligible. Using an average electrostatic model of the solvent, the magnetic shielding constant is calculated as -58.7 ppm, in good agreement with the experimental value of -56.3 ppm. The explicit inclusion of hydrogen-bonded water molecules embedded in the electrostatic field of the remaining solvent molecules gives the value of -61.8 ppm.

First-principles investigation of the alloy scattering potential in dilute Si1-xCx

A first-principles method is applied to find the intra and intervalley n-type carrier scattering rates for substitutional carbon in silicon. The method builds on a previously developed first-principles approach with the introduction of an interpolation technique to determine the intravalley scattering rates. Intravalley scattering is found to be the dominant alloy scattering process in Si1-xCx, followed by g-type intervalley scattering. Mobility calculations show that alloy scattering due to substitutional C alone cannot account for the experimentally observed degradation of the mobility. We show that the incorporation of additional charged impurity scattering due to electrically active interstitial C complexes models this residual resistivity well.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Line search multilevel optimization as computational methods for dense optical flow

We evaluate the performance of different optimization techniques developed in the context of optical flowcomputation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional multilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrectional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimization search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow computation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation.

Line search multilevel optimization as computational methods for dense optical flow

We evaluate the performance of different optimization techniques developed in the context of optical flow computation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we de- velop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional mul- tilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrec- tional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimiza- tion search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow com- putation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation.