About: Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the value function is described by a conic core, a modification of the earlier concept of convex core. Minimizers and generalized minimizers are explicitly constructed from solutions of modified dual problems, not assuming the primal constraint qualification. A-generalized Pythagorean identity is presented using Bregman distance and a correction term for lack of essential smoothness in integrands. Results are applied to minimization of Bregman distances. Existence of a generalized dual solution is established whenever the dual value is finite, assuming the dual constraint qualification. Examples of %22irregular%22 situations are included, pointing to the limitations of generality of certain key results. Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the value function is described by a conic core, a modification of the earlier concept of convex core. Minimizers and generalized minimizers are explicitly constructed from solutions of modified dual problems, not assuming the primal constraint qualification. A-generalized Pythagorean identity is presented using Bregman distance and a correction term for lack of essential smoothness in integrands. Results are applied to minimization of Bregman distances. Existence of a generalized dual solution is established whenever the dual value is finite, assuming the dual constraint qualification. Examples of %22irregular%22 situations are included, pointing to the limitations of generality of certain key results. (en)
Title	Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities (en)
skos:prefLabel	Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities (en)
skos:notation	RIV/67985556:_____/12:00381750!RIV13-AV0-67985556
http://linked.open...avai/predkladatel	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/08/0539), P(GAP202/10/0618)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Matúš, František
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	137834
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/12:00381750
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	maximum entropy; moment constraint; generalized primal/dual solutions; normal integrand; convex duality; Bregman projection; inference principles (en)
http://linked.open.../riv/klicoveSlovo	maximum entropy Bregman projection convex duality generalized primal/dual solutions inference principles moment constraint normal integrand
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[5CF64ECAAB5A]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Conditional independence structures: graphical and algebraic approaches Bregman distances, divergences, and optimal algorithms for information retrieval, decisions and learning
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	48
http://linked.open...iv/tvurceVysledku	Matúš, František Imre, C.
http://linked.open...ain/vavai/riv/wos	000310190200004
issn	0023-5954
number of pages	53 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

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