From linear to convex systems: consistency, Farkas' Lemma and applications

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Title: From linear to convex systems: consistency, Farkas' Lemma and applications
Authors: Dinh, Nguyen | Goberna, Miguel A. | López Cerdá, Marco A.
Research Group/s: Programación Semi-infinita
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Ho Chi Minh City University of Pedagogy. Department of Mathematics-Informatics
Keywords: Convex infinite programming | Constraint qualifications
Knowledge Area: Matemáticas
Date Created: 2005
Issue Date: 2006
Publisher: Heldermann Verlag
Citation: DINH, Nguyen; GOBERNA TORRENT, Miguel Ángel; LÓPEZ CERDÁ, Marco Antonio. “From linear to convex systems: consistency, Farkas' Lemma and applications”. Journal of Convex Analysis. Vol. 13, No. 1 (2006). ISSN 0944-6532, pp. 113-133
Abstract: This paper analyzes inequality systems with an arbitrary number of proper lower semicontinuous convex constraint functions and a closed convex constraint subset of a locally convex topological vector space. More in detail, starting from well-known results on linear systems (with no constraint set), the paper reviews and completes previous works on the above class of convex systems, providing consistency theorems, two new versions of Farkas’ lemma, and optimality conditions in convex optimization. A new closed cone constraint qualification is proposed. Suitable counterparts of these results for cone-convex systems are also given.
Sponsor: This research was partially supported by MCYT of Spain and FEDER of EU, Grant BMF2002-04114- C02-01.
ISSN: 0944-6532
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Appears in Collections:INV - LOPT - Artículos de Revistas

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