Minimization of entropy functionals

TL;DR

This paper investigates the minimization of entropy functionals on convex sets, aiming to weaken the assumptions on constraints while establishing duality and characterization of solutions.

Contribution

It extends the theory of entropy functional minimization by reducing assumptions on the constraint set and providing duality results under weak qualifications.

Findings

Dual equalities established under weak constraint qualifications

Characterization of minimizers achieved with minimal assumptions

Enhanced understanding of entropy functional minimization on convex sets

Abstract

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak constraint qualifications.