Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities

Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bezoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the substantial improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behavior of PENNON

Real-life safety and efficacy of vildagliptin as add-on to metformin in patients with type 2 diabetes in Turkey - GALATA study

PubMed ID: 25697921Objective: To evaluate tolerability/safety and the efficacy of the combination of vildagliptin plus metformin in a real-life population of patients with type 2 diabetes mellitus (T2DM). Research design and methods: This multicenter, single-arm, 6 month, observational, prospective cohort study was conducted at 39 centers across Turkey. T2DM patients on vildagliptin and metformin for ?4 weeks were enrolled regardless of their previous antidiabetic therapy. Main outcome measures: Efficacy was evaluated by measuring hemoglobin A1c (HbA1c) levels. Tolerability/safety parameters evaluated included hypoglycemic events, gastrointestinal events, peripheral edema and weight gain. Results: This study enrolled 665 patients with a mean±standard deviation (SD) age of 55.1±10.2 years and female predominance (n=394, 59.2%). Safety was assessed in all enrolled patients. Hypoglycemia was reported in 10 (1.5%) patients (95% confidence interval = 0.8-2.7%). Efficacy was assessed in 289 (43.5%) patients treated for 6±1 months; these patients showed a mean decrease in HbA1c of 0.8% from baseline value of 7.8% (p65 years) and body mass index (<30 vs. ?30 kg/m2) (p<0.001 each). In total, 136 adverse events (AEs) were observed in 71 (10.7%) patients; 10 (1.5%) patients experienced hypoglycemia and gastrointestinal AEs were most commonly reported (n=29, 4.4%). Conclusions: In a 'real-life' setting, the vildagliptin and metformin combination was associated with significant improvements in reaching target HbA1c levels, even in elderly and obese patients with T2DM. Moreover, vildagliptin and metformin demonstrated a good overall tolerability/safety profile. © 2015 All rights reserved: reproduction in whole or part not permitted.Novartis Pharmaceuticals CanadaThe study was funded by Novartis Pharmaceuticals Turkey. -- The authors thank Cagla Ayhan MD and Prof. Sule Oktay MD PhD from Kappa Consultancy Training Research Ltd, Istanbul, who provided editorial support, and Mehmet Berktas MD MICR from Kappa Consultancy Training Research Ltd, Istanbul, who performed statistical analysis funded by Novartis Pharmaceuticals Turkey. -