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Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
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SYSNO ASEP 0381750 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities Author(s) Csiszár, I. (HU)
Matúš, František (UTIA-B) RIDNumber of authors 2 Source Title Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 48, č. 4 (2012), s. 637-689Number of pages 53 s. Language eng - English Country CZ - Czech Republic Keywords maximum entropy ; moment constraint ; generalized primal/dual solutions ; normal integrand ; convex duality ; Bregman projection ; inference principles Subject RIV BA - General Mathematics R&D Projects GA201/08/0539 GA ČR - Czech Science Foundation (CSF) GAP202/10/0618 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000310190200004 EID SCOPUS 84866016929 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2013
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