Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

Nonsmoothness in Machine Learning: Specific Structure,Proximal Identification,and Applications

Set-Valued and Variational Analysis - Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present...     

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

Engineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real numbers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books.     

Fast screening for presence of muddy/earthy odorants in wine and in wine must using a hyphenated gas chromatography-differential ion mobility spectrometry (GC/DMS)

Rapid, hyphenated detection techniques involving a gas chromatograph (GC) coupled to a classical time-of-flight ion mobility (IMS) spectrometer, or more recently, to a micro-machined, miniature differential ion mobility spectrometer (DMS) are quite attractive for in-situ detection of many kinds of volatile organic compounds (VOCs) of concern and notably of natural contaminants appearing in the headspaces of selected foodstuff. This work aims at a rapid detection, identification and quantification of geosmin in the headspace of grape must and of wine. Samples of white and red wines have both been analyzed with a hyphenated GC/DMS and by Solid Phase Micro-Extraction (SPME) coupled to GC/MS taken as a reference. The detection of geosmin at concentrations below the human olfactory threshold of 50 ng/L has been demonstrated.     

On the Proximal Gradient Algorithm with Alternated Inertia

In this paper, we investigate attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm with alternated inertia, based on local geometric properties of the objective function. The results are put into perspective by discussions on several extensions (strongly convex case, non-convex case, and alternated extrapolation) and illustrations on common regularized optimization problems.     

Newton acceleration on manifolds identified by proximal gradient methods

Mathematical Programming - Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a...     

A branch-and-cut method for the obnoxious p-median problem

The obnoxious p-median (OpM) problem is the repulsive counterpart of the ore known attractive p-median problem. Given a set I of cities and a set J of possible locations for obnoxious plants, a p-cardinality subset Q of J is sought, such that the sum of the distances between each city of I and the nearest obnoxious site in Q is maximised. We formulate (OpM) as a {0,1} linear programming problem and propose three families of valid inequalities whose separation problem is polynomial. We describe a branch-and-cut approach based on these inequalities and apply it to a set of instances found in the location literature. The computational results presented show the effectiveness of these inequalities for (OpM). The work of the first author has been partially supported by the Coordinated Project C.A.M.P.O. and that of the third author by a short mobility grant, both of the Italian National Research Council.     

Existence of a Fixed Point of a Nonsmooth Function Arising in Numerical Mechanics

A recent work (Acary et al. 2010) introduces a formulation as a nonsmooth fixed-point problem of a basic problem in numerical mechanics (namely the dynamical Coulomb friction problem in finite dimension with discretized time). Using this new formulation, the existence of a solution to the problem and its numerical resolution are then guaranteed under a strong assumption on the data of this problem. In this paper, we show that the fixed point problem admits solution under a natural, weaker assumption. This existence proof uses a perturbation argument combined with continuity properties of a set-valued mapping associated with the constraints of the problem.     

Investigation of carbon dioxide modified supercritical and near supercritical carrier streams for flow injection systems

Since flow injection (FI) is a dilution technique, efforts have been undertaken to minimize online dilution or dispersion. Solutes in supercritical fluids exhibit increased diffusion coefficients which have been shown to decrease dispersion of the sample zone. This work investigates the use of supercritical fluids (or CO₂ modified fluids) as carrier streams for FI. Both a non-reacting tracer and an online chemical reaction were employed to investigate the behavior of solutes in supercritical and near critical systems. Further, these results are compared to those obtained in the system studied with a conventional carrier stream. Plots of peak response vs% CO₂ modifier increase with a sharp break at moderate modifier composition (20–30%). Plots of peak variance vs% CO₂ modifier show decreased variance with increasing % modifier. The system was also optimized with regards to temperature and pressure. The optimized system displayed improved limits of detection and decreased variance relative to 0% CO₂ modifier carrier streams.