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

The Influence of Flooding on Contributions of Spartina Alterniflora Roots to Salt Marsh Soil Volume in a Field Setting

Rapid rates of coastal wetland loss in Louisiana are widely recognized. One important question of wetland sustainability is how volumetric contributions of roots to wetland soils vary under the influence of different hydrologic regimes. The research presented here specifically investigates the spatial and temporal relationships among the specific gravity of live roots, soil chemistry, and flooding regime for the macrophyte Spartina alterniflora Loisel. in natural, salt marsh, field settings located across southeastern coastal Louisiana. The results of this research propose the existence of a stress-tolerance threshold (beyond which root specific gravity modifications are observed), and highlight the importance of micro-scale factors over macro-scale regional characteristics in determining environmental stresses and the subsequent impact on root specific gravity. A conceptual model is developed linking the interactions of relevant environmental variables, root specific gravity, and the idea of a stress-tolerance threshold

Ethnic specific obesity cut-offs for diabetes risk: cross-sectional study of 490, 288 UK Biobank participants

OBJECTIVE To compare the relationship between adiposity and prevalent diabetes across ethnic groups in the UK Biobank cohort and to derive ethnic-specific obesity cutoffs that equate to those developed in white populations in terms of diabetes prevalence.<p></p> RESEARCH DESIGN AND METHODS UK Biobank recruited 502,682 U.K. residents aged 40–69 years. We used baseline data on the 490,288 participants from the four largest ethnic subgroups: 471,174 (96.1%) white, 9,631 (2.0%) South Asian, 7,949 (1.6%) black, and 1,534 (0.3%) Chinese. Regression models were developed for the association between anthropometric measures (BMI, waist circumference, percentage body fat, and waist-to-hip ratio) and prevalent diabetes, stratified by sex and adjusted for age, physical activity, socioeconomic status, and heart disease.<p></p> RESULTS Nonwhite participants were two- to fourfold more likely to have diabetes. For the equivalent prevalence of diabetes at 30 kg/m2 in white participants, BMI equated to the following: South Asians, 22.0 kg/m2; black, 26.0 kg/m2; Chinese women, 24.0 kg/m2; and Chinese men, 26.0 kg/m2. Among women, a waist circumference of 88 cm in the white subgroup equated to the following: South Asians, 70 cm; black, 79 cm; and Chinese, 74 cm. Among men, a waist circumference of 102 cm equated to 79, 88, and 88 cm for South Asian, black, and Chinese participants, respectively.<p></p> CONCLUSIONS Obesity should be defined at lower thresholds in nonwhite populations to ensure that interventions are targeted equitably based on equivalent diabetes prevalence. Furthermore, within the Asian population, a substantially lower obesity threshold should be applied to South Asian compared with Chinese groups.<p></p&gt

Letter from Daniel Gill to Henry Spira

I\u27ve reviewed this issue again with our top management team and we are committed to giving it immediate priority. I\u27m sure Barbara will be in touch with you in the next few days with a status report