A Primal-Dual Augmented Lagrangian

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual $\ell$1 linearly constrained Lagrangian (pd$\ell$1-LCL) method

Users Guide for SnadiOpt: A Package Adding Automatic Differentiation to Snopt

SnadiOpt is a package that supports the use of the automatic differentiation package ADIFOR with the optimization package Snopt. Snopt is a general-purpose system for solving optimization problems with many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for large-scale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. The method used by Snopt requires the first derivatives of the objective and constraint functions to be available. The SnadiOpt package allows users to avoid the time-consuming and error-prone process of evaluating and coding these derivatives. Given Fortran code for evaluating only the values of the objective and constraints, SnadiOpt automatically generates the code for evaluating the derivatives and builds the relevant Snopt input files and sparse data structures.Comment: pages i-iv, 1-2

An LDLTLDL^T Trust-Region Quasi-Newton Method

For quasi-Newton methods in unconstrained minimization, it is valuable to develop methods that are robust, i.e., methods that converge on a large number of problems. Trust-region algorithms are often regarded to be more robust than line-search methods, however, because trust-region methods are computationally more expensive, the most popular quasi-Newton implementations use line-search methods. To fill this gap, we develop a trust-region method that updates an $LDL^T$ factorization, scales quadratically with the size of the problem, and is competitive with a conventional line-search method

3D Structures on Relativistic Jets

The properties of wave-like helically twisted normal mode structures on steady relativistic jets are summarized. Wave speeds are a function of the wavelength and less than the jet speed. However, normal mode interference can lead to both stationary and superluminal phase effects. A maximum pressure fluctuation criterion suggested by numerical simulations of axisymmetric relativistic jets is used to find the maximum asymmetric jet distortions and velocity fluctuations. Cyclic transverse velocity fluctuation can lead to variation in the flow direction on the order of the relativistic beaming angle. Resulting variation in the Doppler boost factor can lead to significant brightness asymmetries as helical structures twist around the jet beam. Growth of these structures is reduced as the jet density, Lorentz factor or Mach number are increased. Maximum jet distortion is reduced as the Lorentz factor increases and this suggests a reduction in mass entrainment or other non-linear disruptive processes that influence the morphological development of radio sources.Comment: to appear in Life Cycles of Radio Galaxies, ed. J. Biretta et al., New Astronomy Reviews; 8 pages, including 3 figure

The UK Ministry of Defence Project Orientated Environmental Management System (POEMS)

The Project Orientated Environmental Management System (POEMS) is the UK Ministry of Defence (MoD) bespoke environmental management system for the acquisition and use of equipment. The full implementation of a site-specific environmental management system is challenging for the MoD because there are many permanent MoD sites with transient populations, frequently changing site activities and diverse types of equipment. Nevertheless, MoD policy requires that all sites are covered by an environmental management system. POEMS is based on international standards ISO14001 and ISO14040, which focus on environmental management systems and life cycle assessment, respectively. The primary aim of POEMS is to identify and manage any environmental aspects (causes) and impacts (effects) by scrutinising MoD equipment and activities during acquisition, operation and disposal. This is achieved by drawing up a priority list of activities associated with the equipment based on anticipated environmental impact scores, resulting in an environmental management plan that spans the life cycle of the equipment and any corresponding activities. This article describes the POEMS procedure for both experts and non-experts, and demonstrates the implementation of POEMS using a 105-mm artillery round as a theoretical case study. The results anticipated at each stage of the POEMS procedure are discussed in detail, and the documentation necessary to verify the correct application of POEMS is demonstrated

Association Between Cytokines and Liver Histology in Children with Nonalcoholic Fatty Liver Disease.

BackgroundReliable non-invasive markers to characterize inflammation, hepatocellular ballooning, and fibrosis in nonalcoholic fatty liver disease (NAFLD) are lacking. We investigated the relationship between plasma cytokine levels and features of NAFLD histology to gain insight into cellular pathways driving NASH and to identify potential non-invasive discriminators of NAFLD severity and pattern.MethodsCytokines were measured from plasma obtained at enrollment in pediatric participants in NASH Clinical Research Network studies with liver biopsy-proven NAFLD. Cytokines were chosen a priori as possible discriminators of NASH and its components. Minimization of Akaike Information Criterion (AIC) was used to determine cytokines retained in multivariable models.ResultsOf 235 subjects, 31% had "Definite NASH" on liver histology, 43% had "Borderline NASH", and 25% had NAFLD but not NASH. Total plasminogen activator inhibitor 1 (PAI1) and activated PAI1 levels were higher in pediatric participants with Definite NASH and with lobular inflammation. Interleukin-8 (IL-8) was higher in those with stage 3-4 fibrosis and lobular inflammation. sIL-2rα was higher in children with stage 3-4 fibrosis and portal inflammation. In multivariable analysis, PAI1 variables were discriminators of Borderline/Definite NASH, definite NASH, lobular inflammation and ballooning. IL-8 increased with steatosis and fibrosis severity; sIL-2rα increased with fibrosis severity and portal inflammation. IL-7 decreased with portal inflammation and fibrosis severity.ConclusionsPlasma cytokines associated with histology varied considerably among NASH features, suggesting promising avenues for investigation. Future, more targeted analysis is needed to identify the role of these markers in NAFLD and to evaluate their potential as non-invasive discriminators of disease severity