An algorithm for linearly constrained nonlinear programming problems

In this paper an algorithm for solving a linearly constrained nonlinear programming problem is developed. Given a feasible point, a correction vector is computed by solving a least distance programming problem over a polyhedral cone defined in terms of the gradients of the “almost” binding constraints. Mukai's approximate scheme for computing the step size is generalized to handle the constraints. This scheme provides an estimate for the step size based on a quadratic approximation of the function. This estimate is used in conjunction with Armijo line search to calculate a new point. It is shown that each accumulation point is a Kuhn-Tucker point to a slight perturbation of the original problem. Furthermore, under suitable second order optimality conditions, it is shown that eventually only one trial is needed to compute the step size.     

A precise constant-current coulometer

A precise constant-current coulometer is described suitable for manual or automatic coulometric titrations. The apparatus provides II increments of current in the range 250 μA to 200 mA and gives a standard deviation of better than 30 p.p.m. for the total measurement of coulombs.     

Comparison of glass fragments by neutron activation analysis

A method of comparing glass fragments of potential application to forensic sicence has been developed and evaluated. A representative sample of window glass from England and Wales has been collected and analysed for about 25 elements. An automated radiochemical separation followed by gamma-spectroscopy was used in order to determine the concentration of the maximum number of elements. Frequency distributions of the elemental concentration are shown and used to assess the discrimination of the technique and compare it with the measurement of refractive index. A few simulated cases have been included to demonstrate the possible application to forensic science problems.     

On the convergence of a class of algorithms using linearly independent search directions

Powell has shown that the cyclic coordinate method with exact searches may not converge to a stationary point. In this note we consider a more general class of algorithms for unconstrained minimization, and establish their convergence under the assumption that the objective function has a unique minimum along any line.     

In-situ fractionation—A simple technique for analysis complex mixtures using a routine-gas chromatograph

Summary A simple in-situ fractionation technique, offering several advantages over conventional heart-cutting techniques, is described in which discrete, controlled fractions of effluent from one chromatographic column are transferred sequentially to a second column having diffierent selectively characteristics. Prior to transfer, solutes are stored in-situ on the first column, so that each fraction transferred can be analysed separatley on the second column. In-situ storage and fractionation is achieved using a simple flow-switching arrangement that can be installed in any routine chromatograph without extensive instrument modification. The gas chromatographic determination of aromatics in fuels having final boiling points up to 400° C is used to illustrate the technique. Its potential usefulness in gas chromatography and its possible uses in liquid chromatography are discussed.     

Sweet success: Ionic liquids derived from non-nutritive sweeteners

The anions of the sweeteners saccharin and acesulfame form ionic liquids when paired with a variety of organic cations.     

Nonlinear programming without differentiability in banach spaces: necessary and sufficient constraint qualification

The problem under consideration is a maximization problem over a constraint set defined by a finite number of inequality and equality constraints over an arbitrary set in a reflexive Banach space. A generalization of the Kuhn-Tucker necessary conditions is developed where neither the objective function nor the constraint functions are required to be differentiable. A new constraint qualification is imposed in order to validate the optimality criteria. It is shown that this qualification is the weakest possible in the sense that it is necessary for the optimality criteria to hold at the point under investigation for all families of objective functions having a constrained local maximum at this point