Prox-regular sets and Legendre-Fenchel transform related to separation properties

The Discrete Legendre Fenchel Transform and its application to phase separation in electrolytes

An efficient algorithm for the double Legendre–Fenchel transform with application to phase separation

We study the double discrete Legendre–Fenchel Transform (LFT) to approximate the convex hull of a given function. We analyze the convergence of the double discrete LFT in the multivariate case based on previous convergence results for the discrete LFT by Corrias. We focus our attention on the grid on which the second discrete LFT is computed (dual grid); its choice has great impact on the accur...

The Legendre-Fenchel transform from a category theoretic perspective

The Legendre-Fenchel transform is a classical piece of mathematics with many applications. In this paper we show how it arises in the context of category theory using categories enriched over the extended real numbers R := [−∞,+∞]. A key ingredient is Pavlovic’s “nucleus of a profunctor” construction. The pairing between a vector space and its dual can be viewed as an R-profunctor; the construc...

Legendre-Fenchel duality in elasticity

We show that the displacement and strain formulations of the displacement-traction problem of three-dimensional linearized elasticity can be viewed as Legendre-Fenchel dual problems to the stress formulation of the same problem. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new approach to elasticity by means of Legendre-Fenchel duality. Résumé D...

Regularization of differential variational inequalities with locally prox-regular sets

This paper studies, for a differential variational inequality involving a locally prox-regular set, a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality. The concept of local prox-regularity will be termed in a quantified way, as (r, α)-prox-regularity.