Preprocessing for quadratic programming

Techniques for the preprocessing of (not-necessarily convex) quadratic programs are discussed. Most of the procedures extend known ones from the linear to quadratic cases, but a few new preprocessing techniques are introduced. The implementation aspects are also discussed. Numerical results are finally presented to indicate the potential of the resulting code, both for linear and quadratic problems. The impact of insisting that bounds of the variables in the reduced problem be as tight as possible rather than allowing some slack in these bounds is also shown to be numerically significant.Mathamatics Subject Classification (2000): 20E28, 20G40, 20C20To Roger Fletcher, friend, mentor and inspiration, for his 65th birthday     

Tunable, high-repetition-rate, harmonically mode-locked ytterbium fiber laser

We report a ytterbium fiber laser mode locked at its 281st harmonic, which corresponds to a repetition rate greater than 10 GHz. The laser produces linearly polarized, 2-ps pulses with up to 38-mW of average output power. The mode-locked pulses are tunable over a 58-nm window centered on 1053 nm.     

Enumeration of <Emphasis Type="Italic">P</Emphasis><Subscript>4</Subscript>-Free Chordal Graphs

We count labelled chordal graphs with no induced path of length 3, both exactly and asymptotically. These graphs correspond to rooted trees in which no vertex has exactly one child, and each vertex has been expanded to a clique. Some properties of random graphs of this type are also derived. The corresponding unlabelled graphs are in 1-1 correspondence with unlabelled rooted trees on the same number of vertices. Research supported by the Australian Research Council. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, CanadaResearch carried out while this author was working at CWI and Utrecht University, The Netherlands     

Suppression of analyte signal in inductively-coupled plasma/mass spectrometry and the use of an internal standard

The signal suppression of ⁹Be, ²⁷Al, ⁶⁴Zn, ⁸⁵Rb, ¹¹⁵In and ²⁰⁸Pb in the presence of increasing amounts of sodium chloride is studied. The suppression does not depend significantly on the analyte element considered. The use of ¹¹⁵In as internal standard thus allows correction for the matrix effect. It is shown that the suppressive effect decreases in the order CsCl>NaCl>NH₄Cl. The use of the internal standard also significantly improves the precision. The signal suppression is probably due largely to an increasing number of extracted ions resulting in a more pronounced space-charge effect.     

A note on exploiting structure when using slack variables

We show how to exploit the structure inherent in the linear algebra for constrained nonlinear optimization problems when inequality constraints have been converted to equations by adding slack variables and the problem is solved using an augmented Lagrangian method.This research was supported in part by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No F49620-91-C-0079. The United States Goverment is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.Corresponding author.