Using rank-1 lift-and-project closures to generate cuts for 0–1 MIPs, a computational investigation

Various techniques for building relaxations and generating valid inequalities for pure or mixed integer programming problems without special structure are reviewed and compared computationally. Besides classical techniques such as Gomory cuts, Mixed Integer Rounding cuts, lift-and-project and reformulation–linearization techniques, a new variant is also investigated: the use of the relaxation corresponding to the intersection of simple disjunction polyhedra (i.e. the so-called elementary closure of lift-and-project cuts). Systematic comparative computational results are reported on series of test problems including multidimensional knapsack problems (MKP) and MIPLIB test problems. From the results obtained, the relaxation based on the elementary closure of lift-and-project cuts appears to be one of the most promising.     

The identification of nitrated polycyclic aromatic hydrocarbons in diesel particulate extracts and their potential formation as artifacts during particulate collection

Summary The highly complex matrix of diesel particulate extracts was analyzed for nitrated polycyclic aromatic hydrocarbons (nitro-PAH) using fused-silica capillary-column gas chromatography along with a thermionic nitrogen-phosphorus detector (TID) and high-performance liquid chromatography followed by on-line catalytic reduction of the nitro-PAH to amino-PAH and subsequent fluorescence detection. Positive isomer identification and quantitation of nitro-PAH are from retention times of authentic standards and their mass spectra. The ease of nitro-PAH formation by nitration of PAH raises the question regarding the origin of these species, whether they are produced as “native” products during the engine combustion process and/or in the exhaust, or instead, formed as the result of chemical conversion to produce artifacts during the sampling procedure. This problem is assessed examing 1-nitropyrene-concentration in particulates of three light-duty diesel engines for different sampling times. 1-Nitropyrene concentrations show only a moderate increase with sampling time under average sampling conditions. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Identification of oxygenated polycyclic aromatic hydrocarbons in diesel particulate matter by capillary gas chromatography and capillary gas chromatography/mass spectrometry

Summary Using a two-step liquid chromatographic separation on normalphase cartridges, crude extracts of diesel particulate matter can be separated without time-consuming sample handling into special fractions which mainly contain slightly-polar oxygenated polycyclic aromatic hydrocarbons (oxy-PAH) and nitrated polycyclic aromatic hydrocarbons (nitro-PAH). Subsequent analysis was by fused-silica capillary gas chromatography on a SE54 column along with flame-ionisation (GC/FID) and positive-ion electron-impact mass spectrometric detection (GC/MS) respectively. A number of individual oxy-PAH belonging to four different chemical classes (ketones, quinones, anhydrides and aldehydes) and several individual nitro-PAH were characterized by their retention times and mass spectra. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Anisotropic Analysis of Some Gaussian Models

Although the classical Fractional Brownian Motion is often used to describe porosity, it is not adapted to anisotropic situations. In the present work, we study a class of Gaussian fields with stationary increments and spectral density. They present asymptotic self-similarity properties and are good candidates to model a homogeneous anisotropic material, or its radiographic images. Unfortunately, the paths of all Gaussian fields with stationary increments have the same apparent regularity in all directions (except at most one). Hence we propose here a procedure to recover anisotropy from one realization: computing averages over all the hyperplanes which are orthogonal to a fixed direction, we get a process whose Hölder regularity depends explicitly on the asymptotic behavior of the spectral density in this direction.     

An algorithmic framework for convex mixed integer nonlinear programs

This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported. Both the library of mixed integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried out, and a version of the software used are publicly available.     

Truncations of multilinear Hankel operators

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

     

A note on the MIR closure

In 1988, Nemhauser and Wolsey introduced the concept of MIR inequality for mixed integer linear programs. In 1998, Wolsey gave another definition of MIR inequalities. This note points out that the natural concepts of MIR closures derived from these two definitions are distinct. Dash, Günlük and Lodi made the same observation independently.