Reduction of indefinite quadratic programs to bilinear programs

Indefinite quadratic programs with quadratic constraints can be reduced to bilinear programs with bilinear constraints by duplication of variables. Such reductions are studied in which: (i) the number of additional variables is minimum or (ii) the number of complicating variables, i.e., variables to be fixed in order to obtain a linear program, in the resulting bilinear program is minimum. These two problems are shown to be equivalent to a maximum bipartite subgraph and a maximum stable set problem respectively in a graph associated with the quadratic program. Non-polynomial but practically efficient algorithms for both reductions are thus obtaine.d Reduction of more general global optimization problems than quadratic programs to bilinear programs is also briefly discussed.     

A kinetic model for Brownian motion

Summary The Fokker-Planck equation for the distribution function of a Brownian sphere is derived from the exact hierarchy of kinetic equations for a massive sphere in a bath of smaller spheres, using a multiple-time-scale analysis. Our earlier derivation is specialized to the limiting cases where the bath is either an ideal or Boltzmann gas. The resulting simplifications allow more physical insight, and lead to explicit expressions for the friction coefficient. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

On using estimates of Lipschitz constants in global optimization

Several authors have proposed estimating Lipschitz constants in global optimization by a multiple of the largest slope (in absolute value) between successive evaluation points. A class of univariate functions is exhibited for which the global optimum will be missed when using such a procedure, even if the multiple is arbitrarily large.Research of the first and third authors was supported by AFOSR Grants 0271 and 0066 to Rutgers University. Research of the second author was supported by NSERC Grant GP0036426 and FCAR Grant 90NC0305.This research was done while the first author was Professor and the third author was Graduate Student at RUTCOR, Rutgers University.     

Testing integer knapsacks for feasibility

We present a new approach for determining whether there exist nonnegative integers x₁, x₂, …, x_n satisfying a₁x₁ + a₂x₂ + ? + a_nx_n = b, where a₁ < a₂ < ? < a_n and b are nonnegative integers. case time complexity is analyzed and compared with dynamic programming techniques. Computational results are given.     

Exploitation of gradient techniques in flow injection analysis

Summary Founded on the key role of dispersion, controlled in space and time, the FIA gradient techniques are based on the feasibility of identifying and selecting reproducibly suitable sections of the time/concentration matrix represented by the dispersed sample zone and exploiting the specific concentrations at these points for analytical purposes. The characteristics and common theme of these gradient procedures — comprising gradient dilution and calibration, stopped flow reaction rate measurement, titrations, gradient scanning, and systems associated with simultaneous injection of two zones which completely or partially overlap thereby permitting the execution of selectivity studies and standard addition procedures — are briefly reviewed.

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Ausnutzung von Gradientenverfahren bei der Fließinjektionsanalyse