Generalized minimizers of convex integral functionals and Pythagorean identities

I. Csiszár, František Matúš

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages302-307
Number of pages6
Volume8085 LNCS
DOIs
Publication statusPublished - 2013
Event1st International SEE Conference on Geometric Science of Information, GSI 2013 - Paris, France
Duration: Aug 28 2013Aug 30 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8085 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other1st International SEE Conference on Geometric Science of Information, GSI 2013
CountryFrance
CityParis
Period8/28/138/30/13

Fingerprint

Pythagorean identity
Integral Functionals
Constraint Qualifications
Minimizer
Convex Duality
Bregman Distance
Integrand
Value Function
Moment
Term

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Csiszár, I., & Matúš, F. (2013). Generalized minimizers of convex integral functionals and Pythagorean identities. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8085 LNCS, pp. 302-307). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8085 LNCS). https://doi.org/10.1007/978-3-642-40020-9_32

Generalized minimizers of convex integral functionals and Pythagorean identities. / Csiszár, I.; Matúš, František.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8085 LNCS 2013. p. 302-307 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8085 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Csiszár, I & Matúš, F 2013, Generalized minimizers of convex integral functionals and Pythagorean identities. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8085 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8085 LNCS, pp. 302-307, 1st International SEE Conference on Geometric Science of Information, GSI 2013, Paris, France, 8/28/13. https://doi.org/10.1007/978-3-642-40020-9_32
Csiszár I, Matúš F. Generalized minimizers of convex integral functionals and Pythagorean identities. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8085 LNCS. 2013. p. 302-307. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-40020-9_32
Csiszár, I. ; Matúš, František. / Generalized minimizers of convex integral functionals and Pythagorean identities. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8085 LNCS 2013. pp. 302-307 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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