In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.
Keywords: Entropy maximisation problems, Bayesian statistics, application in engineering
@article{RO_2021__55_2_355_0,
author = {Gamboa, Fabrice and Gu\'eneau, Christine and Klein, Thierry and Lawrence, Eva},
title = {Maximum {Entropy} on the {Mean} approach to solve generalized inverse problems with an application in computational thermodynamics},
journal = {RAIRO. Operations Research},
pages = {355--393},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {2},
doi = {10.1051/ro/2021005},
mrnumber = {4234138},
zbl = {1472.90088},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021005/}
}
TY - JOUR AU - Gamboa, Fabrice AU - Guéneau, Christine AU - Klein, Thierry AU - Lawrence, Eva TI - Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics JO - RAIRO. Operations Research PY - 2021 SP - 355 EP - 393 VL - 55 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021005/ DO - 10.1051/ro/2021005 LA - en ID - RO_2021__55_2_355_0 ER -
%0 Journal Article %A Gamboa, Fabrice %A Guéneau, Christine %A Klein, Thierry %A Lawrence, Eva %T Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics %J RAIRO. Operations Research %D 2021 %P 355-393 %V 55 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021005/ %R 10.1051/ro/2021005 %G en %F RO_2021__55_2_355_0
Gamboa, Fabrice; Guéneau, Christine; Klein, Thierry; Lawrence, Eva. Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics. RAIRO. Operations Research, Tome 55 (2021) no. 2, pp. 355-393. doi: 10.1051/ro/2021005
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