Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems*

In this paper, the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth. Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance. Moreover, the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an (affine-scaled) Clarke stationary point of the original nonsmooth and nonconvex problem. Their experimental results indicate the effectiveness of the proposed algorithm.     

Products and transforms of white-noise functionals (in general setting)

Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990).     

On the global optimization properties of finite-difference local descent algorithms

The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special -convex structure. It is assumed that the objective function can be closely approximated by some smooth convex function. Stability properties of the perturbed gradient descent and coordinate descent methods are investigated. Basing on this results some global optimization properties of finite-difference local descent algorithms, in particular, coordinate descent method, are discovered. These properties are not inherent in methods using exact gradients.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Computerized optimization of gradient elution conditions with ternary solvent mobile phases in RPLC

Summary In this work, an optimization procedure for gradient RPLC separation, using ternary mobile phases, is described. This procedure requires eight preliminary experiments in gradient elution mode to predict the retention surface for each solute over the whole triangular space. This is followed by computerized calculations to determine the best ternary gradient elution profile with respect to both selectivity and analysis time. The efficiency of this procedure from the point of view of rapidity and of accuracy, is illustrated for the specific separation of twelve phenyl urea herbicides.     

Gradients of the Exchange-repulsion Energy in the General Effective Fragment Potential Method

Formulae for calculating the analytic gradients of the exchange-repulsion energy in the general effective fragment potential (EFP2) method are derived and implemented using a direct differentiation approach. The timings for the exchange repulsion gradient evaluations are approximately three times longer than the energy evaluations, orders of magnitude faster than a previous implementation. Since the direct differentiation approach is not approximate, the gradients can be used with confidence in molecular dynamics and Monte Carlo simulations with the EFP2 method.     

Tests for liquid chromatographs

Summary The paper describes tests for liquid chromatographs to assess the autosampler and pump flow rate precision; suitability of the instrument for normal phase chromatography; UV detector performance; and external band broadening characteristics. Tests for mixing and proportioning characteristics of solvent pumps and performance of diode array detectors are also considered. These tests are designed to evaluate the performance of both newly released liquid chromatography equipment and equipment already in operation. Data from evaluations carried out by instrument manufacturer’s and suppliers is reported and discussed. This data offers specifications to a common format for initial selection of instruments prior to purchase.     

Comparison of the sequential simplex method and linear solvent strength theory in HPLC gradient elution optimization of multicomponent flavonoid mixtures

Summary Using a camomile flavonoid extract as the sample and four different reversed-phase partition systems, the ability of the Simplex procedure to produce optimum gradient separation of unknown multicomponent mixtures was checked against the linear solvent strength (LSS) gradient elution theory. On the same partition systems the mean solvent strenghts were measured by experimentally determined logk vs. mobile phase composition plots. These mean solvent strengths are compared to those inferred from the optimum gradients and the usefulness of LSS theory in multicomponent mixture gradient elution optimization is discussed.Dadicated to Prof. Dr. A Liberti on the occasion of his 70th birthday.     

New approach to linear gradient elution used for optimisation in reversed-phase liquid chromatography

A new mathematical treatment concerning the gradient elution in reversed-phase liquid chromatography when the volume fraction psi of an organic modifier in the water-organic mobile phase varies linearly with time is presented. The experimental ln k versus psi curve, where k is the retention factor under isocratic conditions in a binary mobile phase, is subdivided into a finite number of linear portions and the solute gradient retention time tR is calculated by means of an analytical expression arising from the fundamental equation of gradient elution. The validity of the proposed analytical expression and the methodology followed for the calculation of tR was tested using eight catechol-related solutes with mobile phases modified by methanol or acetonitrile. It was found that in all cases the accuracy of the predicted gradient retention times is very satisfactory because it is the same with the accuracy of the retention times predicted under isocratic conditions. Finally, the above method for estimating gradient retention times was used in an optimisation algorithm, which determines the best variation pattern of psi that leads to the optimum separation of a mixture of solutes at different values of the total elution time.     

Simultaneous determination of rosiglitazone and metformin in plasma by gradient liquid chromatography with UV detection

A novel, fast and simple liquid chromatographic method was developed and validated for the simultaneous determination of rosiglitazone and metformin in human plasma. The analysis was performed on a phenyl column (250 mm × 4.6 mm i.d., 5 μm) using a gradient method starting with mobile phase composed of acetonitrile:5 mM acetate buffer pH 5.5 (75:25, v/v). The flow rate was 1 mL min⁻¹. UV detection was performed at 245 nm and verapamil was used as internal standard. The total run time was less than 10 min. Sample preparation included a simple protein precipitation step with acetonitrile. Validation experiments were performed to demonstrate stability, specificity, sensitivity, linearity, accuracy, precision and robustness. The limit of quantification was 100 ng mL⁻¹ for rosiglitazone and 250 ng mL⁻¹ for metformin. The extraction recoveries were 100.02-105.0% for rosiglitazone and 105.64-103.88% for metformin. The method was applied with success to plasma samples obtained from diabetic patients undergoing treatment with rosiglitazone and metformin.