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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F12%3A00381750" target="_blank" >RIV/67985556:_____/12:00381750 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

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

Original language 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 andgeneralized 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 "irr

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Kybernetika

ISSN

0023-5954

e-ISSN

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Volume of the periodical

48

Issue of the periodical within the volume

4

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

53

Pages from-to

637-689

UT code for WoS article

000310190200004

EID of the result in the Scopus database

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