Počet záznamů: 1
Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
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SYSNO ASEP 0381750 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities Tvůrce(i) Csiszár, I. (HU)
Matúš, František (UTIA-B) RIDCelkový počet autorů 2 Zdroj.dok. Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 48, č. 4 (2012), s. 637-689Poč.str. 53 s. Jazyk dok. eng - angličtina Země vyd. CZ - Česká republika Klíč. slova maximum entropy ; moment constraint ; generalized primal/dual solutions ; normal integrand ; convex duality ; Bregman projection ; inference principles Vědní obor RIV BA - Obecná matematika CEP GA201/08/0539 GA ČR - Grantová agentura ČR GAP202/10/0618 GA ČR - Grantová agentura ČR Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000310190200004 EID SCOPUS 84866016929 Anotace 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 "irregular" situations are included, pointing to the limitations of generality of certain key results. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2013
Počet záznamů: 1