0397249 20240103203059.220131112235959.9 10.1007/978-3-642-40020-9_32 6 s. P cav_un_epca*0398425978-3-642-40019-30302-9743302-307BerlinSpringer2013 Integral functional convex normal integrand primal constraint qualification generalized minimizer Pythagorean identities information geometry cav_un_auth*0015571 Csiszár I. 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/2013/MTR/http://library.utia.cas.cz/separaty/2013/MTR/matus-0397249.pdf Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. 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. The minimizers and generalized minimizers are explicitly described whenever the primal value is finite, assuming a dual constraint qualification but not the primal constraint qualification. A generalized Pythagorean identity is presented using Bregman distance and a correction term. cav_un_auth*0294821 Geometric Science of Information 2013 Paris 28.08.2013-30.08.2013 FR 2014 BD 2 PR RVO:67985556 http://hdl.handle.net/11104/0225900 100 0.325 16.75 0.51 Q2 Q3 2013 cav_un_epca*0398425 Geometric Science of Information 2013 978-3-642-40019-3 0302-9743 302 307 Berlin Springer 2013 Lecture Notes in Computer Science 8085