LEAST CHANGE UPDATE METHODS FOR NONLINEAR-SYSTEMS WITH NONDIFFERENTIABLE TERMS

We extend the local convergence theory of least change secant update methods given by Martinez (Mathematics of Computation 55, 143-167, 1990) to nonlinear systems with nondifferentiable terms as studied by Zabrejko and Nguen (Numerical Functional Analysis and Optimization 9, 671-684, 1987), Chen and Yamamoto in a sequence of recent papers.144173240541

Algorithms for Solving Nonlinear Systems of Equations

In this paper we survey numerical methods for solving nonlinear systems of equations F (x) = 0, where F : IR n ! IR n . We are especially interested in large problems. We describe modern implementations of the main local algorithms, as well as their globally convergent counterparts. 1. INTRODUCTION Nonlinear systems of equations appear in many real - life problems. Mor'e [1989] has reported a collection of practical examples which include: Aircraft Stability problems, Inverse Elastic Rod problems, Equations of Radiative Transfer, Elliptic Boundary Value problems, etc.. We have also worked with Power Flow problems, Distribution of Water on a Pipeline, Discretization of Evolution problems using Implicit Schemes, Chemical Plant Equilibrium problems, and others. The scope of applications becomes even greater if we include the family of Nonlinear Programming problems, since the first-order optimality conditions of these problems are nonlinear systems. Given F : IR n ! IR n ; F = (..

Regular Wine Consumption in Chronic Heart Failure: Impact on Outcomes, Quality of Life, and Circulating Biomarkers

Background-Moderate, regular alcohol consumption is generally associated with a lower risk of cardiovascular events but data in patients with chronic heart failure are scarce. We evaluated the relations between wine consumption, health status, circulating biomarkers, and clinical outcomes in a large Italian population of patients with chronic heart failure enrolled in a multicenter clinical trial. Methods and Results-A brief questionnaire on dietary habits was administered at baseline to 6973 patients enrolled in the Gruppo Italiano per lo Studio della Sopravvivenza nell'Insufficienza Cardiaca-Heart Failure (GISSI-HF) trial. The relations between wine consumption, fatal and nonfatal clinical end points, quality of life, symptoms of depression, and circulating biomarkers of cardiac function and inflammation (in subsets of patients) were evaluated with simple and multivariable-adjusted statistical models. Almost 56% of the patients reported drinking at least 1 glass of wine per day. After adjustment, clinical outcomes were not significantly different in the predefined 4 groups of wine consumption. However, patients with more frequent wine consumption had a significantly better perception of health status (Kansas City Cardiomyopathy Questionnaire score, adjusted P<0.0001), less frequent symptoms of depression (Geriatric Depression Scale, adjusted P=0.01), and lower plasma levels of biomarkers of vascular inflammation (osteoprotegerin and C-terminal proendothelin-1, adjusted P<0.0001, and pentraxin-3, P=0.01) after adjusting for possible confounders. Conclusions-We show for the first time in a large cohort of patients with chronic heart failure that moderate wine consumption is associated with a better perceived and objective health status, lower prevalence of depression, and less vascular inflammation, but does not translate into more favorable clinical 4-year outcomes. Clinical Trial Registration-URL: http://www.clinicaltrials.gov. Unique identifier: NCT0033633