Generalized minimizers of convex integral functionals and Pythagorean identities

0397249 - ÚTIA 2014 RIV DE eng C - Conference Paper (international conference)
Csiszár, I. - Matúš, František
Generalized minimizers of convex integral functionals and Pythagorean identities.
Geometric Science of Information 2013. Berlin: Springer, 2013, s. 302-307. Lecture Notes in Computer Science, 8085. ISBN 978-3-642-40019-3. ISSN 0302-9743.
[Geometric Science of Information 2013. Paris (FR), 28.08.2013-30.08.2013]
Institutional support: RVO:67985556
Keywords : Integral functional * convex normal integrand * primal constraint qualification * generalized minimizer * Pythagorean identities * information geometry
Subject RIV: BD - Theory of Information
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.
Permanent Link: http://hdl.handle.net/11104/0225900