0381751 20240103201335.920121105235959.9 000312544300031 10.1109/ISIT.2012.6283516 5 s. P cav_un_epca*0382541978-1-4673-2579-02157-8095150-154CambridgeIEEE2012 maximum entropy moment constraint primal/dual solutions normal integrand convex duality Bregman projection generalized exponential family cav_un_auth*0284663 Imre C. HU cav_un_auth*0101161 Matúš František Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2012/MTR/matus-minimization of entropy functionals revisited.pdf GA201/08/0539 GA ČR cav_un_auth*0239648 GAP202/10/0618 GA ČR cav_un_auth*0263481 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. cav_un_auth*0285167 IEEE International Symposium on Information Theory Proceedings (ISIT), 2012 Cambridge 01.07.2012-06.07.2015 US 2013 BA 2 PR RVO:67985556 http://hdl.handle.net/11104/0007173 2012 000312544300031 WOS cav_un_epca*0382541 Proceedings of the IEEE International Symposium on Information Theory Proceedings (ISIT), 2012 978-1-4673-2579-0 2157-8095 150 154 Cambridge IEEE 2012