Generalized minimizers of convex integral functionals and Pythagorean identities

Imre 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 publicationGeometric Science of Information - First International Conference, GSI 2013, Proceedings
Pages302-307
Number of pages6
DOIs
Publication statusPublished - Oct 8 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Csiszár, I., & Matúš, F. (2013). Generalized minimizers of convex integral functionals and Pythagorean identities. In Geometric Science of Information - First International Conference, GSI 2013, Proceedings (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