Lagrangian relaxation is a tool to find upper bounds on a given (arbitrary) maximization
problem. Sometimes, the bound is exact and an optimal solution is found. Our aim in this …

Given a finite number of moments of an unknown density ̄x on a finite measure space, the
best entropy estimate—that nonnegative density x with the given moments which minimizes …

Best entropy estimation is a technique that has been widely applied in many areas of
science. It consists of estimating an unknown density from some of its moments by …

This article presents a new approach for detecting active sources in the cortex from magnetic
field measurements on the scalp in magnetoencephalography (MEG). The solution of this ill …

We discuss several moment closure models for linear kinetic equations that have been
developed over the past few years as alternatives to classical spectral and collocation …

Nonparametric density estimation aims to determine the sparsest model that explains a
given set of empirical data and which uses as few assumptions as possible. Many of the …

Entropy-based (MN) moment closures for kinetic equations are defined by a constrained
optimization problem that must be solved at every point in a space–time mesh, making it …

These lecture notes are an extension of those given in the master programs at the
Universities Paris VI and Paris-Saclay, and in the École Polytechnique. They give an …

We present a new entropy-based moment method for the velocity discretization of kinetic
equations. This method is based on a regularization of the optimization problem defining the …

Entropy-based methods are widely used for solving inverse problems, particularly when the
solution is known to be positive. Here, we address linear ill-posed and noisy inverse …