Calcul sous-differentiel et optimisation

Any amenable $\text{C}{}^1$ algebra is nuclear. Injective von Neumann algebras are characterized by the vanishing of their cohomology with coefficients in dual normal Banach bimodules.     

Convergence of asymptotic directions

We study convergence properties of asymptotic directions of unbounded sets in normed spaces. The links between the continuity of a set-valued map and the convergence of asymptotic directions are examined. The results are applied to investigate continuity properties of marginal functions and asymptotic directions of level sets.

     

Subdifferentiation of integral functionals

Mathematical Programming - We examine how the subdifferentials of nonconvex integral functionals can be deduced from the subdifferentials of the corresponding integrand or at least be estimated...     

Subdifferentiation of Regularized Functions

We study the Moreau regularization process for functions satisfying a general growth condition on general Banach spaces. We give differentiability criteria and we study the relationships between the subdifferentials of the function and the subdifferentials of its approximations. We also consider the Lasry-Lions process.     

Preservation of persistence and stability under intersections and operations,part 2: Stability

The stability of the image of a moving convex set by a multifunction is considered. This study completes the persistence results obtained in Part 1 of this paper (Ref. 1). The results can be applied to epigraphs, hence to the convergence of convex functions.     

Experiments in the mixed convection regime in an isothermal open cubic cavity

A detailed experimental study of the heat transfer in an open isothermal cubic cavity for mixed natural and forced convection is reported. First the experimental model with a temperature control system, the experimental procedure, and the method for determination of the convective heat losses from the experimental data are presented. After presentation of the experimental conditions for the three models of different sizes that were tested, dimensionless parameters (Gr, Re, and Nu numbers) are introduced to generalize the results. In this way, the main influence of natural convection can be separated, and, using regressional analysis, a general interdependence among Nusselt, Reynolds, and Grashof numbers can be obtained.

The local heat transfer effects are indicated by maps of local heat transfer coefficient distributions in the cavity for different orientations of the model. To reduce the effects of convective heat transfer, the influence of different types of front masks were analyzed. The usefulness of the experimental results obtained is shown by estimating the convective heat losses for the central solar receiver of the French solar power plant THEMIS.     

The Compatibility with Order of Some Subdifferentials

It is well known that elementary subdifferentials which are the simplest and the most precise among known subdifferentials do not enjoy good calculus rules, whereas more elaborated subdifferentials do have calculus rules but are not as precise and, in particular, do not preserve order. This paper explores an order preservation property for the subdifferentials of the second category. This property concerns the case in which a distance function is involved. It emphasizes the crucial role played by such functions in nonsmooth analysis. The result enables one to get in a simple, unified way the passage from the properties of subdifferentials for Lipschitzian functions to the same properties for the case of lower semicontinuous functions.     

The directional subdifferential of the difference of two convex functions

We provide a criterion giving a formula for the directional (or contingent) subdifferential of the difference of two convex functions. We even extend it to the difference of two approximately starshaped functions. Our analysis relies on a notion of approximate monotonicity for operators which is much less demanding than the usual one.     

Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps

We establish connections between some concepts of generalized monotonicity for set-valued maps introduced earlier and some notions of generalized convexity. Moreover, a notion of pseudomonotonicity for set-valued maps is introduced; it is shown that, if a function f is continuous, then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar.