Linear representations and quasipolyhedrality of a finite-valued convex function

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Title: Linear representations and quasipolyhedrality of a finite-valued convex function
Authors: Fajardo Gómez, María Dolores | López Cerdá, Marco A. | Puente, Rubén
Research Group/s: Programación Semi-infinita
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad Nacional de San Luis (Argentina). Departamento de Matemáticas
Keywords: Semi-infinite linear inequality systems | Quasipolyhedral convex sets | Suddifferential set | Conjugate function | Valadier formula
Knowledge Area: Matemáticas
Issue Date: Apr-2008
Publisher: Taylor & Francis
Citation: FAJARDO GÓMEZ, María Dolores; LÓPEZ CERDÁ, Marco Antonio; PUENTE, Rubén. “Linear representations and quasipolyhedrality of a finite-valued convex function”. Optimization. Vol. 57, Issue 2 (Jan. 2008). ISSN 0233-1934, pp. 215-237
Abstract: The possibility of representing the epigraph of a finite-valued convex function by means of a (locally) Farkas-Minkowski linear semi-infinite inequalities system is studied in this article. Moreover, we prove that the so-called locally polyhedral representations characterize the function, giving rise to the concept of quasipolyhedral function. Conditions for its conjugate to be also quasipolyhedral are obtained, as well as the characterization of its subdifferential and eps-subdifferential in terms of an specific sequence of ordinary polyhedral functions.
ISSN: 0233-1934 (Print) | 1029-4945 (Online)
DOI: 10.1080/02331930701779864
Language: eng
Type: info:eu-repo/semantics/article
Rights: This is an electronic version of an article published in Optimization ©2008 Copyright Taylor & Francis; Optimization is available online at
Peer Review: si
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