A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Nerve fiber layer in glaucomatous hemifield loss: a case-control study with time- and spectral-domain optical coherence tomography

Purpose: To evaluate the retinal nerve fiber layer measurements with time-domain (TD) and spectral-domain (SD) optical coherence tomography (OCT), and to test the diagnostic ability of both technologies in glaucomatous patients with asymmetric visual hemifield loss. Methods: 36 patients with primary open-angle glaucoma with visual field loss in one hemifield (affected) and absent loss in the other (non-affected), and 36 age-matched healthy controls had the study eye imaged with Stratus-OCT (Carl Zeiss Meditec Inc., Dublin, California, USA) and 3 D OCT-1000 (Topcon, Tokyo, Japan). Peripapillary retinal nerve fiber layer measurements and normative classification were recorded. Total deviation values were averaged in each hemifield (hemifield mean deviation) for each subject. Visual field and retinal nerve fiber layer "asymmetry indexes" were calculated as the ratio between affected versus non-affected hemifields and corresponding hemiretinas. Results: Retinal nerve fiber layer measurements in non-affected hemifields (mean [SD] 87.0 [17.1] mu m and 84.3 [20.2] mu m, for TD and SD-OCT, respectively) were thinner than in controls (119.0 [12.2] mu m and 117.0 [17.7] mu m, P<0.001). The optical coherence tomography normative database classified 42% and 67% of hemiretinas corresponding to non-affected hemifields as abnormal in TD and SD-OCT, respectively (P=0.01). Retinal nerve fiber layer measurements were consistently thicker with TD compared to SD-OCT. Retinal nerve fiber layer thickness asymmetry index was similar in TD (0.76 [0.17]) and SD-OCT (0.79 [0.12]) and significantly greater than the visual field asymmetry index (0.36 [0.20], P<0.001). Conclusions: Normal hemifields of glaucoma patients had thinner retinal nerve fiber layer than healthy eyes, as measured by TD and SD-OCT. Retinal nerve fiber layer measurements were thicker with TD than SD-OCT. SD-OCT detected abnormal retinal nerve fiber layer thickness more often than TD-OCT.

DXA, bioelectrical impedance, ultrasonography and biometry for the estimation of fat and lean mass in cats during weight loss

Background: Few equations have been developed in veterinary medicine compared to human medicine to predict body composition. The present study was done to evaluate the influence of weight loss on biometry (BIO), bioimpedance analysis (BIA) and ultrasonography (US) in cats, proposing equations to estimate fat (FM) and lean (LM) body mass, as compared to dual energy x-ray absorptiometry (DXA) as the referenced method. For this were used 16 gonadectomized obese cats (8 males and 8 females) in a weight loss program. DXA, BIO, BIA and US were performed in the obese state (T0; obese animals), after 10% of weight loss (T1) and after 20% of weight loss (T2). Stepwise regression was used to analyze the relationship between the dependent variables (FM, LM) determined by DXA and the independent variables obtained by BIO, BIA and US. The better models chosen were evaluated by a simple regression analysis and means predicted vs. determined by DXA were compared to verify the accuracy of the equations. Results: The independent variables determined by BIO, BIA and US that best correlated (p < 0.005) with the dependent variables (FM and LM) were BW (body weight), TC (thoracic circumference), PC (pelvic circumference), R (resistance) and SFLT (subcutaneous fat layer thickness). Using Mallows'Cp statistics, p value and r(2), 19 equations were selected (12 for FM, 7 for LM); however, only 7 equations accurately predicted FM and one LM of cats. Conclusions: The equations with two variables are better to use because they are effective and will be an alternative method to estimate body composition in the clinical routine. For estimated lean mass the equations using body weight associated with biometrics measures can be proposed. For estimated fat mass the equations using body weight associated with bioimpedance analysis can be proposed.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.