Metric Subregularity in Generalized Equations

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.     

Effect of matrices and additives on phosphorylated and ketodeoxyoctonic acid lipids A analysis by matrix‐assisted laser desorption ionization‐mass spectrometry

Lipid A is a major compound of the outer membrane of gram‐negative bacteria and is a key factor of bacterial virulence. As lipid A's structure differs among bacterial species and varies between strains of the same species, knowing its modifications is essential to understand its implications in the infectious process. To analyze these lipids, matrix‐assisted laser desorption ionization‐mass spectrometry (MALDI‐MS) is a well‐suited method that is fast and efficient. However, there are limitations with the matrix and additives used, such as the suppression of signal or prompt fragmentations that could give a false overview of lipid A composition in biological samples. For a comprehensive analysis of the entire lipid A species present in a sample, we tested 16 matrices and 11 additives on two commercial lipids A. The first commercial one contains single phosphorylation group, and the second contains two phosphorylation and two ketodeoxyoctonic acid (KDO) groups. The lipid A containing KDO groups was essentially detected by the 3‐hydroxypicolinic acid (3‐HPA) matrix, whereas the monophosphorylated lipid A could be detected by 13 matrices out of the 16. We also demonstrated that the signal of diphosphorylated lipid A can be enhanced with the use of additives in the matrix. Our study indicated that the best conditions to obtain a clear signal of both lipids A without prompt fragmentation was the use of 3‐HPA with 10mM trifluoroacetic acid (TFA).     

Spectral Convex Functions of Operators and Approximate Intertwining Relationships

We develop theoretical tools for the analysis of convex spectral functions of non-symmetric operators on Hilbert spaces. The obtained results are applied to an optimization problem arising from the theory of inverse problems, which involves the notion of intertwining relationship.     

Synergistic extraction of europium and americium into nitrobenzene by using hydrogen dicarbollylcobaltate and 1,2-(diphenylphosphino)ethane dioxide

Extraction of microamounts of europium and americium by a nitrobenzene solution of hydrogen dicarbollylcobaltate (H⁺B⁻) in the presence of 1,2-(diphenylphosphino)ethane dioxide (DPPEtDO, L) has been investigated. The equilibrium data have been explained assuming that the species HL⁺, HL₂ ⁺, ML₂ ³⁺ and ML₄ ³⁺ (M³⁺ = Eu³⁺, Am³⁺) are extracted into the organic phase. The values of extraction and stability constants of the species in nitrobenzene saturated with water have been determined. It was found that the stability constants of the corresponding complexes EuL _n ³⁺ and AmL _n ³⁺, where n = 2, 4 and L is DPPEtDO, in water-saturated nitrobenzene are comparable.     

An inexact bundle variant suited to column generation

We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous—so that zero is a natural Slater point—and an exact oracle may be time consuming. Finally, our convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems. Research supported by INRIA New Investigation Grant “Convex Optimization and Dantzig–Wolfe Decomposition”.     

Kinetic Study on Models of the Noncatalyzed Reaction Between α, ω -Dicarboxypolyamide-11 and α, ω -Dihydroxypolyoxyalkylenes

The kinetics of the noncatalyzed reaction between α, ω -dicarboxypoly-amide-11 and α, ω -dihydroxypolyoxyalkylenes is investigated by using the reactions of 11-dodecylamidoundecanoic acid with 1-dodecanol, 2-tridecanol, α-dodecyl-ω-hydroxypolyoxyethylene or α-dodecyl-ω;-hydroxypolyoxypropylene as models. Kinetic data fit a 3rd overall order (2 in acid and 1 in alcohol). Rate constants and activation parameters are determined and compared.     

Robust network design in telecommunications under polytope demand uncertainty

We consider a model for robust network design in telecommunications, in which we minimize the cost of the maximum mismatch between supply and demand. In the present study, the demand is uncertain and takes its values in a polytope defined by constraints. This problem is hardly tractable, so we limit ourselves to computing lower bounds (by a column-generation mechanism) and upper bounds (using an algorithm due to Falk and Soland for maximizing a separable convex function over a polytope). The experimental gap obtained turns out to be large, and this seems to be mainly due to poor upper bounds. Two possible solutions are suggested for further research aimed at improving them: dc optimization (to minimize the difference of two convex functions) and AARC modeling (affinely adjustable robust counterpart).     

Comparison of bundle and classical column generation

When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method; our aim is to illustrate its differences with Kelley’s method. In the process we review alternative stabilization techniques used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm. This research has been supported by Inria New Investigation Grant “Convex Optimization and Dantzig-Wolfe Decomposition”.     

Probing particle-particle interactions in flocculated oil-in-water emulsions using ultrasonic attenuation spectrometry

The flocculation of silicone oil-in-water emulsions ( φ = 0.1) containing quasi-monodisperse droplets was studied by ultrasound. The ultrasonic attenuation spectra of emulsions with different particle sizes (200-1600 nm) were measured between 0.5 and 10 MHz using an interferometer. Flocculation was induced by adding excess sodium dodecyl sulphate micelles to the emulsions to increase the attractive forces between the droplets. Droplet flocculation decreased the ultrasonic attenuation at low frequencies because of overlap of the thermal waves caused by the close proximity of the droplets within the flocs. A mean-field model which takes into account this effect was used to determine the droplet volume fraction within the flocs and thus to estimate the distance between the droplets. Received 17 July 2000