Minimization of Entropy Functionals Revisited

0381751 - ÚTIA 2013 RIV US eng C - Conference Paper (international conference)
Imre, C. - Matúš, František
Minimization of Entropy Functionals Revisited.
Proceedings of the IEEE International Symposium on Information Theory Proceedings (ISIT), 2012. Cambridge: IEEE, 2012, s. 150-154. ISBN 978-1-4673-2579-0. ISSN 2157-8095.
[IEEE International Symposium on Information Theory Proceedings (ISIT), 2012. Cambridge (US), 01.07.2012-06.07.2015]
R&D Projects: GA ČR GA201/08/0539; GA ČR GAP202/10/0618
Institutional support: RVO:67985556
Keywords : maximum entropy * moment constraint * primal/dual solutions * normal integrand * convex duality * Bregman projection * generalized exponential family
Subject RIV: BA - General Mathematics
http://library.utia.cas.cz/separaty/2012/MTR/matus-minimization of entropy functionals revisited.pdf

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are assumed to be strictly convex but not autonomous or differentiable. The effective domain of the value function is described by a modification of the concept of convex core. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. Main results assume a dual constraint qualification but dispense with the primal constraint qualification. Minimizers and generalized minimizers are explicitly described whenever the primal value is finite. Existence of a generalized dual solution is established whenever the dual value is finite. A generalized Pythagorean identity is presented using Bregman distance and a correction term. Results are applied to minimization of Bregman distances.
Permanent Link: http://hdl.handle.net/11104/0007173