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.

Description and evaluation of a Newton-based electronic appetite rating system for temporal tracking of appetite in human subjects

This study assessed the reliability and validity of a palm-top-based electronic appetite rating system (EARS) in relation to the traditional paper and pen method. Twenty healthy subjects [10 male (M) and 10 female (F)] — mean age M=31 years (S.D.=8), F=27 years (S.D.=5); mean BMI M=24 (S.D.=2), F=21 (S.D.=5) — participated in a 4-day protocol. Measurements were made on days 1 and 4. Subjects were given paper and an EARS to log hourly subjective motivation to eat during waking hours. Food intake and meal times were fixed. Subjects were given a maintenance diet (comprising 40% fat, 47% carbohydrate and 13% protein by energy) calculated at 1.6×Resting Metabolic Rate (RMR), as three isoenergetic meals. Bland and Altman's test for bias between two measurement techniques found significant differences between EARS and paper and pen for two of eight responses (hunger and fullness). Regression analysis confirmed that there were no day, sex or order effects between ratings obtained using either technique. For 15 subjects, there was no significant difference between results, with a linear relationship between the two methods that explained most of the variance (r2 ranged from 62.6 to 98.6). The slope for all subjects was less than 1, which was partly explained by a tendency for bias at the extreme end of results on the EARS technique. These data suggest that the EARS is a useful and reliable technique for real-time data collection in appetite research but that it should not be used interchangeably with paper and pen techniques.

Operational performance of low-cost carriers and international airlines : New evidence using a bootstrap truncated regression

Between 2001 and 2005, the US airline industry faced financial turmoil. At the same time, the European airline industry entered a period of substantive deregulation. This period witnessed opportunities for low-cost carriers to become more competitive in the market as a result of these combined events. To help assess airline performance in the aftermath of these events, this paper provides new evidence of technical efficiency for 42 national and international airlines in 2006 using the data envelopment analysis (DEA) bootstrap approach first proposed by Simar and Wilson (J Econ, 136:31-64, 2007). In the first stage, technical efficiency scores are estimated using a bootstrap DEA model. In the second stage, a truncated regression is employed to quantify the economic drivers underlying measured technical efficiency. The results highlight the key role played by non-discretionary inputs in measures of airline technical efficiency.

Efficiency of research performance of Australian universities : a reappraisal using a bootstrap truncated regression approach

The motivation of the study stems from the results reported in the Excellence in Research for Australia (ERA) 2010 report. The report showed that only 12 universities performed research at or above international standards, of which, the Group of Eight (G8) universities filled the top eight spots. While performance of universities was based on number of research outputs, total amount of research income and other quantitative indicators, the measure of efficiency or productivity was not considered. The objectives of this paper are twofold. First, to provide a review of the research performance of 37 Australian universities using the data envelopment analysis (DEA) bootstrap approach of Simar and Wilson (2007). Second, to determine sources of productivity drivers by regressing the efficiency scores against a set of environmental variables.

Efficiency and productivity of Singapore’s manufacturing sector 2001-2010: An analysis using Simar and Wilson’s (2007) bootstrapped truncated approach

This paper seeks to explain the lagging productivity in Singapore’s manufacturing noted in the statements of the Economic Strategies Committee Report 2010. Two methods are employed: the Malmquist productivity to measure total factor productivity change and Simar and Wilson’s (J Econ, 136:31–64, 2007) bootstrapped truncated regression approach. In the first stage, the nonparametric data envelopment analysis is used to measure technical efficiency. To quantify the economic drivers underlying inefficiencies, the second stage employs a bootstrapped truncated regression whereby bias-corrected efficiency estimates are regressed against explanatory variables. The findings reveal that growth in total factor productivity was attributed to efficiency change with no technical progress. Most industries were technically inefficient throughout the period except for ‘Pharmaceutical Products’. Sources of efficiency were attributed to quality of worker and flexible work arrangements while incessant use of foreign workers lowered efficiency.

Relative abundance of full-length and truncated FOXP1 isoforms is associated with differential NFκB activity in Follicular Lymphoma

FOXP1 is a transcriptional repressor that has been proposed to repress the expression of some NFκB-responsive genes. Furthermore, truncated forms of FOXP1 have been associated with a subtype of Diffuse Large B-cell Lymphoma characterised by constitutive NFκB activity, indicating that they may inhibit this repression. We have shown that FL tumors have increased relative abundance of truncated FOXP1 isoforms and this is associated with increased expression of NFκB-associated genes. Our results provide strong evidence that relative FOXP1 isoform abundance is associated with NFκB activity in FL, and could potentially be used as a marker for this gene signature.

Efficiency and productivity of Singapore's manufacturing sector 2001-2010 : an analysis using bootstrapped truncated approach

This paper seeks to explain the lagging productivity in Singapore’s manufacturing noted in the statements of the Economic Strategies Committee Report 2010. Two methods are employed: the Malmquist productivity to measure total factor productivity (TFP) change and Simar and Wilson’s (2007) bootstrapped truncated regression approach which first derives bias-corrected efficiency estimates before being regressed against explanatory variables to help quantify sources of inefficiencies. The findings reveal that growth in total factor productivity was attributed to efficiency change with no technical progress. Sources of efficiency were attributed to quality of worker and flexible work arrangements while the use of foreign workers lowered efficiency.

Replicating satellite RNA induces sequence-specific DNA methylation and truncated transcripts in plants

Tobacco plants were transformed with a chimeric transgene comprising sequences encoding β-glucuronidase (GUS) and the satellite RNA (satRNA) of cereal yellow dwarf luteovirus. When transgenic plants were infected with potato leafroll luteovirus (PLRV), which replicated the transgene-derived satRNA to a high level, the satellite sequence of the GUS:Sat transgene became densely methylated. Within the satellite region, all 86 cytosines in the upper strand and 73 of the 75 cytosines in the lower strand were either partially or fully methylated. In contrast, very low levels of DNA methylation were detected in the satellite sequence of the transgene in uninfected plants and in the flanking nonsatellite sequences in both infected and uninfected plants. Substantial amounts of truncated GUS:Sat RNA accumulated in the satRNA-replicating plants, and most of the molecules terminated at nucleotides within the first 60 bp of the satellite sequence. Whereas this RNA truncation was associated with high levels of satRNA replication, it appeared to be independent of the levels of DNA methylation in the satellite sequence, suggesting that it is not caused by methylation. All the sequenced GUS:Sat DNA molecules were hypermethylated in plants with replicating satRNA despite the phloem restriction of the helper PLRV. Also, small, sense and antisense ∼22 nt RNAs, derived from the satRNA, were associated with the replicating satellite. These results suggest that the sequence-specific DNA methylation spread into cells in which no satRNA replication occurred and that this was mediated by the spread of unamplified satRNA and/or its associated 22 nt RNA molecules.